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Date Blue Hill Meteorological Observatory Historical Chronology
1776 Although the name "Blue Hill" was in use prior to this time, an act of the Massachusetts legislature declared that the summit be named Great Blue Hill. Beacons were established and the summit was used as a vantage point during the Revolutionary War.
1798, May 30 Construction began on a forty-foot stone and wood observing platform. It was blown down four years later, rebuilt, again repaired in 1822 and then remained for many years.
1830 A state trigonometric survey conducted by Simeon Borden precisely established the position of Great Blue Hill and the height above mean sea level as 193.69 m (635.05 feet).
1845, July The Corps of Engineers of the U.S Coast Survey opened a new road to the summit near the site of the current road.
1861, Jan 6 Founder of the Blue Hill Observatory, Abbott Lawrence Rotch, was born in Boston, Massachusetts.
1861, Mar 12 Henry Helm Clayton, observer from 1886 to 1909, was born in Murfreesboro, Tennessee.
1863, Aug 3 Alexander George McAdie, Observatory director from 1913 to 1931, was born in New York City.
1884, May Rotch graduated from the Massachusetts Institute of Technology with a degree in engineering.
1884, Aug 5 Rotch first documented the idea of building a weather observatory on Great Blue Hill.
1884, Sep 1 Construction began on the original observatory, which consisted of a two-story tower and living quarters.
1885, Feb 1 The Observatory was occupied and official daily observations began on the summit.
1886, Jan A Campbell-Stokes sunshine recorder, the first of its kind in the United States was first used. It remained in service until it was replaced in July, 1993.
1888, Jan 1 The oldest mercury barometer still in daily use at the Observatory (number 872), which was purchased by Rotch in London and brought to Blue Hill in December 1887, was first put into service. It was later moved from the first floor to the second floor of the tower.
1889 The east wing addition to the Observatory, which was started on 18 October, 1888, was completed in early 1889. The upper floor of the addition served as the original library.
1891 Government weather agency was shifted from the Signal Service to the Weather Bureau under the Department of Agriculture.
1893 The Metropolitan District Commission acquired land around the Blue Hills for parkland that would become the Blue Hills Reservation.
1894, Aug 4 The first atmospheric sounding in the world was accomplished at Blue Hill with a kite carrying a thermograph to a height of 2030 feet above mean sea level.
1897, Mar 6 A kerosene-powered, steam-driven windlass was first used at Blue Hill for kite soundings.
1898, Feb 1 An unusually heavy snowstorm brought 20 inches of snow in about 24 hours, which was the largest snowstorm on record until 1958.
1900, Jul 19 The highest kite sounding in the world was made from Blue Hill to a height of 4,815 m (15,790 feet).
1901, Aug 22 First kite soundings over water with made with trial flights over Massachusetts Bay.
1901, Aug 28 First kite soundings over the open ocean were made to a height of 700 m (2,300 feet) from an eastbound trans-atlantic steamer by Rotch and Sweetland.
1902, Nov The west wing addition to the Observatory, which was started on 31 March, 1902, was completed.
1903, Jun 26 The new library was opened in the recently completed west wing. This room was finished with a tile vaulted ceiling of the style that originated with the Guastovino family in Spain. In the corners near the ceiling were placed eight bas-reliefs representing the allegorical figures of the winds that were on the first century B.C. Tower of the Winds in Athens.
1904 An instrument called an "ombroscope", which was designed to record the time of precipitation, was first put in regular service. The present ombroscope at Blue Hill dates from the 1940s.
1904, Sep 15 The first balloonsonde in the United States was arranged by Rotch and launched by Fergusson at the St. Louis Louisiana Purchase Exposition.
1905, April 17 The Hazen instrument shelter was moved to its present location northeast of the Observatory and a fenced enclosure was set up around the shelter, rain gages and other outdoor instruments.
1905, May 16 Construction of a concrete wall and installation of a gated, iron fence around the Observatory was completed at the cost of $2000.
1906, Jan A pioneer in the development of meteorology, Norweigian scientist Vilhelm Bjerknes, visited the Observatory, where he witnessed a kite flight and discussed the vertical structure of the atmosphere with Rotch.
1906, Sep 1 Rotch was appointed as the first Professor of Meteorology at Harvard.
1907 Rotch became the first president of the Aero Club of New England.
1907, Oct 23 Clayton and Erbslock win balloon race with record flight from St. Louis to Asbury Park, New Jersey by covering 1,410 km (876 miles) in forty hours (an American record at the time). Clayton used wind measurements from a balloonsonde preceding the race to guide the balloon to favorable westerly winds.
1908, Jun 4 Construction was completed of a new three-story concrete tower at a cost of $5000. Demolition of the original two-story tower had been started on 25 March.
1910 Rotch publishes his book Conquest of the Air, an up-to-date and historical summary of dirigible balloons, flying machines and the future of aerial navigation. In December 1909, Rotch received a letter from Wilbur Wright commending the book.
1912, Apr 7 Abbott Lawrence Rotch dies suddenly from an undiagnosed ruptured appendix.
1913, Mar Harvard University takes over operation of the Observatory with an endowment of $50,000 from Rotch.
1913, Oct 1 Alexander George McAdie was appointed as Director of the Observatory.
1914, Jan 16 Wiring the Observatory for electricity was completed and electric lights were first placed in service.
1914, Jul 17 A stone monument to Rotch designed by Bela L. Pratt was erected on the summit of Great Blue Hill. The inscription reads: "In memory of Abbott Lawrence Rotch, founder of the Blue Hill Observatory, pioneer in the study of the upper air, a life devoted to science for the good of mankind."
1918, Oct 1 In recognition of his teaching, McAdie was appointed the first Abbott Lawrence Rotch Professor of Meteorology at Harvard.
1919 McAdie receives letters from the Navy and from Franklin D. Roosevelt, then Assistant Secretary of the Navy, commending his work training officers in aerography and weather observing at Blue Hill during World War I.
1919 Charles Franklin Brooks was a co-founder and the first secretary of the American Meteorological Society in Boston.
1924, Jan A series of three storms each with strong winds near 80 mph seriously damaged the copper sheathing on the Observatory roof, which was not fully repaired until April.
1931 McAdie retired and Charles Franklin Brooks was appointed as the third director of the Observatory.
1932, Oct The Mount Washington Observatory in New Hampshire was opened.
1933, Nov 7 Daily radio communications were established between Blue Hill and Mt. Washington.
1934, Feb 9 The coldest temperature ever measured at Blue Hill, -21 deg F, was observed.
1934, Feb The coldest month on record at the Observatory with an average temperature of 13.5 deg F was observed.
1934, Apr 12 The Mt. Washington record wind gust of 231 mph was timed by radio at Blue Hill.
1935, Feb 1 Observatory's 50th anniversary; Brooks proposed the development of the radio-meteorograph to transmit atmospheric measurements from sounding balloons to the surface.
1935, Apr 17 The first radio-meteorograph transmission of temperature data from an airplane was received at Blue Hill from a height of 17,000 feet.
1935, Nov Carl-Gustaf Rossby, then a Professor of Meteorology at MIT, visited Blue Hill to observe progress in the development of the radio-meteorograph.
1935, Dec 23 The first radio-meteorograph transmission of pressure and temperature data from a balloon was received at Blue Hill from a height of 52,500 feet.
1936, Aug 19 German airship Hindenburg was observed from Blue Hill passing about one mile to the west at 11:20 AM and heading west of south. It was just below the cumulus clouds at about 2000 feet.
1937, May 6 German airship Hindenburg was seen entering clouds as it passed east of Blue Hill at about 10:45 AM headed for Lakehurst, New Jersey where it met with tragedy later in the day.
1938, Sep 21 Great New England hurricane brought the highest wind gust ever experienced at Blue Hill. Numerous readings by several observers of the Draper wind recording established a top five-minute average wind speed of 121 mph from the south at 6:11 to 6:16 P.M. EST. From this a peak gust of 186 mph was calculated with an uncertainty of 30 to 40 mph. The highest hourly average wind speed was 84 mph from 5 to 6 P.M. Precipitation at Blue Hill during the storm was light and amounted to 0.12 inch.
1941, Dec 14 Following the attack on Pearl Harbor, eight U.S. Army personnel arrived at Blue Hill and manned the post 24 hours a day to spot and report airplanes and to collect upper air wind measurements. They left the Observatory for another location about one month later.
1943-44 Brooks and John H. Conover participated in a program for the Weather Bureau to instruct civilian and military weather observers throughout the United States on cloud observing and to make these reports more valuable to forecasters.
1946 A steel extension was added to the south side of the Observatory tower roof to serve as a platform for various solar radiation instruments.
1946, Oct 26 Henry Helm Clayton, who was associated with the Observatory from 1886-1909 and 1943-1946, died at age 85.
1948, Jan 25 Heavy snowfalls during the winter of 1947-48 accumulated to a peak average snow depth of 42 inches on the summit, which remained the deepest snow depth observed until March 1969.
1948 The first Observatory government contract with the Weather Bureau provided funding to the Observatory for one year to perform research related to snowstorm forecasting.
1949, Aug 10 An unusually hot summer peaked with a high temperature of 101 deg F, the highest ever recorded at Blue Hill. This was later matched on Aug 2, 1975.
1951, Oct 6 Non-commercial radio station WGBH-FM first went on the air transmitting from a storage room under the library in the Observatory. The 95-foot high transmitting tower was erected on the rocks to the northwest of the tower. The call letters "WGBH" were named for Great Blue Hill.
1953, Jun 9 Debris from the Worcester tornado fell at Blue Hill. Oak twigs with frayed leaves were followed by papers, rags, shingles, roofing paper, insulation, boards up to 12 feet long, and pieces of walls or roofs a meter square (3×3 feet). This material had been carried 25-38 miles by the storm.
1954, Apr 21 The WGBH-FM transmitter facility was moved from the Observatory to a separate building on the summit to the southeast of the tower, which had been completed in January.
1954, Aug 31 Hurricane Carol brought a peak wind gust on Blue Hill of 125 mph from the southeast.
1954, Nov 16 U.S. Air Force Geophysical Research Directorate established a weather radar laboratory on the summit that remained until November, 1961.
1954, Dec 11 A new WGBH FM and TV transmission tower near the new building was completed. Total height of the new tower and antenna was 71.6 m (235 feet).
1955, May 2 WGBH TV first went on the air.
1955, Aug 19 Former Hurricane Diane passed New England as a tropical storm, but it brought record rainfall of 9.93 inches in 24 hours and 12.77 inches for the storm total over a period of 57 hours.
1957, Sep 1 Dr. Charles F. Brooks retired as director; John H. Conover was appointed acting director, and he continued in that position through June 1958.
1958, Jan 8 Dr. Charles F. Brooks died suddenly at his home at age 66.
1958, Jan 16 A snowstorm brought 22.2 inches of snow in 22 hours, which was the largest snowfall from a single storm on record through that date.
1958, Jul 1 Richard M. Goody of Harvard was appointed director of the Observatory.
1958, Oct The Observatory library was removed and distributed to various libraries and to the Weather Bureau, with a significant portion being moved to the Gordon McKay Library at Harvard where it remains.
1959, Jun 1 Weather Bureau took over operation of the climatological observations.
1959, Aug 26 The Observatory's mercury barometers were raised 9.4 feet from the first to the second floor of the Observatory tower during the process of moving the weather office to the second floor.
1959, Nov 16 Sterling Price Fergusson died at age 91.
1960, Sep 12 Hurricane Donna brought a peak wind gust of 140 mph from the south-southeast to Blue Hill, the second highest gust ever recorded at the Observatory. The fastest mile for the day, which is the speed of the passage of one mile of wind in the shortest time, was 92 mph also from the SSE.
1962 The first measurements of airglow, the emission of radiation from atomic oxygen during the day, were made at Blue Hill by Goody and John Noxon.
1962 A siderostat, which directed the solar beam by means of a motorized mirror to indoor instruments, was erected at the rear of the west wing of the Observatory. The structure, without its original mirrors, remains in its original location to this day.
1966 Successful spectroscopic measurements of the concentration of nitrous oxide in the atmosphere were made by Noxon.
1968, Mar 13 One of the most significant ice storms to affect the Observatory left one-inch thick ice accumulation on all surfaces.
1968 Goody first documented interest in ending Harvard's association with the Observatory in part due to the interference from the WGBH transmitter with ongoing research.
1969, Feb A monthly snowfall total of 65.4 inches was measured. This included the snowfall record for a single storm, 38.7 inches, which fell over four days from the 24th to the 28th. This was the monthly record until 83.6 inches was recorded in February 2015.
1969, Mar 4 A new record snow depth of 43 inches was measured. This remained the record until it was surpassed in February 2015.
1970, Jan 2 The National Weather Service, formerly the Weather Bureau, appointed William Cusick as official-in-charge of the station.
1971, Oct 1 After considerable effort and discussion, the National Weather Service agreed to continue operation of the Observatory, and ownership of the facility was transferred from Harvard to the Metropolitan District Commission. Goody retired as director.
1975, Aug 2 The highest temperature ever recorded at the Observatory, 101 deg F, was measured, matching a temperature observed on Aug 10, 1949.
1976, Jan 1 Observatory was officially listed as a Reference Climatological Station by the World Meteorological Organization due to the length and homogeneity of its climate record.
1977, May 10 The heaviest late-season snowfall on record occurred with 7.8 inches being measured on the summit.
1978, Feb 7 The great "Blizzard of 1978" brought 30.1 inches of snow in 33 hours ending on the 7th. Snow depth on the ground was 33 inches on the morning of the 8th. The fastest mile during the storm was 67 mph from the northeast, with gusts from the NE on the evening of the 6th estimated to about 80 mph.
1978, May 1 William Cusick retired and Robert Skilling, who had served as relief observer since October 1960, was appointed as chief observer.
1980, Feb 26 Preservation of the historic Blue Hill weather archives and paper recordings was accomplished by their transfer to permanent residence at the U.S. National Archives facilty in Waltham.
1980, Sep 27 Observatory was placed on the National Register of Historic Places.
1981, Feb 13 The barometric pressure, reduced to sea level, reached 1052.4 mb (31.08 inches) a new record high pressure at the Observatory.
1981, Jun The Blue Hill Observatory Weather Club and Museum was established by Dr. William Minsinger to support the preservation and restoration of the facility and to hold meetings for local amateurs and professionals to discuss the weather.
1985, Feb 1 100th anniversary of the Observatory was celebrated by over a hundred guests with presentations on the history of the station, with the re-dedication of the Rotch Memorial monument, which had been inscribed with a summary of the weather from the past century, and with fireworks in the evening.
1985, Sep 27 Hurricane Gloria made landfall in western New England and brought a peak wind gust to 100 mph to the Observatory. The wind has not reached that magnitude again since that date.
1988 Blue Hill Weather Club President, William E. Minsinger, publishesThe 1938 Hurricane: An Historical and Pictorial Summary on the 50th anniversary of the Great New England Hurricane.
1989, Dec The Blue Hill Meteorological Observatory was recognized as a National Historic Landmark by the U.S. National Park Service.
1990 Former Blue Hill observer and Director, John H. Conover, publishes The Blue Hill Meteorological Observatory: The First 100 Years, 1885-1985.
1993, Jul The original Campbell-Stokes sunshine recorder was reported stolen from the tower roof on the 11th and replaced with a modern duplicate instrument. The original was recovered in a few days and remains on display in the Observatory history room.
1996, Apr 10 The seasonal snowfall total reached 144.4 inches during the last storm of the 1995-96 season. This was the seasonal record until the winter of 2014-2015 when 150.8 inches was measured.
1997, Apr 1 Greatest 24-hour snowfall on Blue Hill of 30.0 inches, which began on March 31st, was measured.
1997, Sep Extensive renovations of the Observatory began.
1998 A new annual precipitation record of 71.00 inches was established.
1998, May Observatory first developed an Internet web site (www.bluehill.org).
1998, Oct 15 The Automated Surface Observing System (ASOS) operated by the National Weather Service to provide hourly automated weather observations was commissioned at Blue Hill as station ID KMQE.
1998 With support from private grants, the Observatory began the WINS (Women in Natural Science) Program, a series of educational programs designed to inspire adolescent females to pursue careers in math and science.
1998, Dec The Blue Hill Observatory Science Center was established to expand the Observatory's mission to include atmospheric science education. William E. Minsinger became President and Charles T. Orloff was named Executive Director of the non-profit organization.
1999, May 1 Completion of the extensive Observatory renovations was celebrated with a public Open House and Grand Re-Opening ceremonies.
2000, Oct 21 Blue Hill Science Center co-sponsored the First Southern New England Weather Conference, an annual meeting of professionals and amateurs designed to enhance communication among various local groups with an interest in the weather.
2002, Jan The American Meteorological Society recognized the Observatory with its Award for Outstanding Services to Meteorology by a Corporation. The inscription read, "for its distinguished history of meteorological research and commitment to maintaining a high-quality climate record, and its dedication to increasing public understanding of atmospheric science."
2003 Environmental Protection Agency (EPA) installed ozone measuring equipment on Blue Hill for local air quality monitoring.
2003, Dec 30 Former Blue Hill Director and observer, John H. Conover, whose association with the Observatory began in the 1930s, died at age 87.
2004, Oct Observatory began participating in CAMNET, a regional network of high-resolution "visibility" cameras viewable on the Internet, to raise public awareness about the effects of pollution on visibility.
2004, Oct 4 Blue Hill hosted the U.S. Postal Service's First Day of Issue ceremonies for the release of the "Cloudscapes" sheet of twenty stamps depicting various cloud types.
2006, Feb Blue Hill Observatory first announced plans for a new environmental Science Center facility to be located on the summit of Great Blue Hill.
2010, Feb 1 Observatory celebrated its 125th Anniversary with invited lectures by Dr. Louis Uccellini, Paul Kocin and others on January 30th, along with a reception and fireworks on the summit on the evening of the 30th. An Open House with additional festivities was held at the Observatory on January 31st and February 1st.
2010, Mar A new monthly precipitation record for any month of the year of 18.81 inches was established. This included the second highest single-storm rainfall total on record at the Observatory of 9.41 inches on March 13th-15th, 2010.
2010, Jul The warmest month on record at the Observatory with an average temperature of 75.1 deg F was observed.
2012 The warmest year on record at the Observatory was established with a mean of 51.7 deg F.
2013, Mar 8 The second of two blizzards within a month ends with a total of 29.8 inches on March 6-8th. A blizzard on February 8-9th had brought a total of 26.6 inches to the Observatory.
2015, Jan 28 The second largest snowstorm in the Observatory's history ended with a total of 30.8 inches measured on January 26-28th.
2015, Feb The snowiest month on record was established with a total of 83.6 inches of snow at the Observatory, surpassing the previous record of 65.4 inches in February, 1969. This included two of the largest snowstorms ever to occur in February, which brought 27.7 inches on February 7-10th and 21.6 inches on February 14-15th. A record snow depth of 46 inches was measured on February 15th.
2015, Mar A new record for the snowiest season on record at the Observatory was established with a total of 150.8 inches, surpassing the previous record of 144.4 inches in 1995-1996.
2015, Dec A new record was established for the greatest positive temperature departure for any month since 1885. This month was the warmest December on record and 13.1 degrees F warmer than the 1891-2010 120-year average.
2016, Feb 14 A daily record minimum temperature of -14 deg F was the coldest recorded at the Observatory since -16 deg F occurred on January 15, 1957. With a high temperature of 10 deg F and a mean of -2 deg F, this day was the coldest Valentine's Day on record at Blue Hill.
2016, Feb 16 The high temperature climbed to 55 deg F, producing a 69 deg F increase in temperature in less than 72 hours from the low of -14 deg F on the 14th. This change matched the previous record for a temperature swing within three days when the mercury rose from -18 deg F on the morning December 30, 1933 to 51 deg F on January 1, 1934.
2017, Feb 24 A new record high temperature for the month of February, 71 deg F, was observed on the 24th, which surpassed the previous record for February and for the date of 68 deg F set in 1985. This was also the earliest in any year that a temperature of 70 deg F or higher has been recorded.
2017, May The Observatory was recognized as a Centennial Observing Station by the World Meteorological Organization.
2017, May 18 A new record high temperature for May, 96 deg F, was observed on the 18th.
2018, Mar 13 A record calendar day snowfall for March of 23.0 inches was observed.This amount tied as the fourth greatest storm total snowfall in March.
2018, Nov 22 The coldest Thanksgiving Day on record was observed with a high temperature of 20 deg F and a low temperature of 9 deg F.
2020, Jan 12 The record warmest temperature ever observed in January, 68 deg F, was tied, matching the previous occurrence of this temperature on January 26, 1950. Combined with 65 deg F observed on January 11, 2020, these were the warmest consecutive pair of days ever observed in January.
2021, Jun A major renovation of the Observatory commences.


text:
\section{Introduction}

The $s = 1/2$ antiferromagnetic (AFM) Heisenberg model on the two-dimensional
kagome lattice is one of the simplest models in frustrated quantum magnetism,
but displays some of the most complex behavior known.\cite{review} As such,
it has for decades maintained its position at the forefront in the search
for novel quantum-mechanical phases of matter, such as the
resonating-valence-bond (RVB) spin-liquid state proposed initially by
Anderson.\cite{Anderson} The nature of the ground state of the $s = 1/2$
kagome AFM has still not been fully established: the variety of competing
phases proposed in the literature includes valence-bond crystals
(VBCs),\cite{VBS} gapped spin liquids,\cite{SL1,SL2,SL3} and gapless
critical phases.\cite{CP1,CP2} Under these circumstances, the discovery
that the kagome AFM is extremely sensitive even to the smallest perturbations,
such as the presence of anisotropies\cite{Elhajal,Ballou} or of non-magnetic
impurities,\cite{Dommange,Lauchli} is completely consistent.

In this context, the recent discovery\cite{Shores} of the mineral
herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$, has attracted very considerable
attention, because it represents a structurally perfect realization of
the $s = 1/2$ kagome AFM. This material is composed of Cu$^{2+}$ ions
($s = 1/2$) arranged on kagome planes separated by triangular layers
of non-magnetic Zn$^{2+}$ ions. Despite the large AFM exchange, $J \simeq
170$-190 K in this material,\cite{Rigol,Misguich} in experiment there is
no evidence of long-ranged magnetic order or even of spin freezing at any
temperatures down to 50 mK.\cite{muons,Helton} There is in addition no
sign of a spin gap in the excitation spectrum.\cite{Helton,Olariu}

However, it has also been established that in ZnCu$_3$(OH)$_6$Cl$_2$ there
is a significant (5-10\%) intersite exchange of Cu$^{2+}$ ions with the
Zn$^{2+}$ ions intended to separate the kagome planes.\cite{impurities1,
impurities2} The displaced Cu$^{2+}$ ions are thought to account for the
large Curie tails observed in powder susceptibility measurements\cite{Bert,
Helton} and for the field-dependent, Schottky-like anomaly in the specific
heat.\cite{impurities2} At the same time, the Zn$^{2+}$ ions displaced
into the kagome planes play the role of non-magnetic vacancies, which are
known\cite{Dommange,Lauchli} to modify the ground state properties in a
nontrivial way. However, these impurities can also be considered as a probe
of kagome physics, and in this respect the recent $^{17}$O nuclear magnetic
resonance (NMR) experiments reported by Olariu {\it et al.}\cite{Olariu}
offer extensive insight. While each O$^{2-}$ ion is coupled predominantly
to two neighboring Cu$^{2+}$ ions in the kagome planes, the NMR spectra
revealed a broad distribution of local susceptibilities. The relative 1:2
ratio between the line shifts of the two leading features in the $^{17}$O
spectrum was explained on the basis of distinguishing between two groups
of O sites in the doped kagome planes, those [``Defect'' (D)] probing the
magnetic polarization directly next to an impurity site, and hence coupled
only to one Cu spin, and those [``Main'' (M)] reflecting the polarizations
of all other sites. This interpretation was also consistent with the
relative intensities of the two lines based on the expected in-plane
dopant concentration of approximately 5\%. Another major finding of these
experiments was the observation that the (M) and (D) line shifts approach
a finite value as $T \to 0$, suggesting a non-singlet ground state without
a gap. This result can also be inferred from the non-activated behavior
of the nuclear spin-lattice relaxation rate, $1/T_1$, at low
temperatures.\cite{Olariu}

While the true nature of the non-magnetic ground state of the pure,
$s = 1/2$ Heisenberg kagome AFM remains unknown, all of the guidance
obtained from VBC or RVB constructions suggests a total singlet. Indeed,
the nearest-neighbor RVB basis has been shown to deliver a semi-quantitative
account of some of the properties of the system, both without\cite{SL2,rmm}
and with\cite{Dommange} impurities, and for this reason a non-singlet ground
state presents a considerable challenge. However, by the nature of its
structure, a triangular geometry involving active $d_{x^2-y^2}$ and
$d_{3z^2-r^2}$ orbitals, the Cu--Cu bonds in ZnCu$_3$(OH)$_6$Cl$_2$ are
not centrosymmetric. The resulting Dzyaloshinskii-Moriya (DM)
interactions\cite{DM} induce quite generally a small admixture of triplet
states into a singlet ground state,\cite{Rigol} and thus have been
discussed\cite{Olariu} as a likely explanation for the finite response
observed at zero temperature. The DM interactions in herbertsmithite have
been determined recently by electron spin resonance experiments.\cite{Zorko}
These measurements show that the dominant component of the DM interaction is
that perpendicular to the kagome plane, which is of order $D \simeq 15$ K
$\sim 0.08 J$, while the in-plane component, $D'$, although not excluded
by symmetry, is much smaller ($D'\simeq 2$ K $\sim 0.01 J$).

Clearly, a complete theoretical description for the ground-state properties
of ZnCu$_3$(OH)$_6$Cl$_2$, including the magnetization response around the
impurity sites, must take into account the combined effect of both the DM
interactions and the non-magnetic impurities in the kagome planes. Among
the many approaches adopted to gain further insight into the kagome system,
it is well known that the clean, classical kagome AFM without DM anisotropy
has an extensive ground-state degeneracy,\cite{Moessner_Review_Class_Deg}
which is fully lifted by quantum fluctuations only beyond harmonic
order.\cite{HarrisKallinBerlinsky,Chubukov,ChanHenley} The inclusion of
DM anisotropy perpendicular to the kagome plane selects immediately the
uniform ($Q = 0$), three-sublattice state.\cite{Elhajal,Ballou} C\'epas
{\it et al.} have shown recently\cite{Cepas} that in the quantum ($s = 1/2$)
kagome AFM, this ordered phase can be stabilized only for $D/J \gtrsim 0.1$.
This implies that herbertsmithite may well be very close to the critical
point where quantum fluctuation effects promote a disordered ground state.
The linear susceptibility of the clean kagome AFM in the presence of DM
interactions has been analyzed\cite{Tovar} using a perturbative expansion
about a short-ranged VBC ground-state scenario, while the effect of
non-magnetic impurities without DM interactions has been studied in
Refs.~[\onlinecite{Dommange,Lauchli,Gregor,Rozenberg}].
It has been shown that one of the central consequences of a non-magnetic
impurity in the quantum kagome AFM is a characteristic dimer freezing,
which takes place around the impurity site due to frustration relief in
the affected triangles.\cite{Dommange,Lauchli}

Here we present an extensive exact-diagonalization study which includes
the effects of both DM anisotropy and non-magnetic impurities. Our results
can be summarized as follows. For $D/J \lesssim 0.06$, the effect of
frustration relief around the impurity\cite{Dommange,Lauchli} causes the
formation of strong, local dimers whose magnetization response, a staggered
moment directed along $\mathbf{D} \times \mathbf{B}$, is qualitatively similar to
that of isolated dimers. In this regime we find surprisingly large variations
in the magnitude of the response on the different induced dimers. For sites
far away from the impurity, we argue that the response must be uniform and
much smaller in magnitude. For $D/J \gtrsim 0.1$, the system enters the
$Q = 0$, 120$^\circ$, semiclassically ordered state,\cite{Elhajal,Ballou,
Cepas} and the effect of impurities becomes very short-ranged. However,
even here we find that the dimers next to the impurity remain strong up
to values $D/J\sim 1$, meaning that their spins remain correlated with
each other, rather than participating in the ordered state, for $D/J
\lesssim 1$.

\begin{figure}[!b]
\includegraphics[width=0.45\textwidth]{Kagome}
\caption{(Color online) The kagome lattice of Cu$^{2+}$ ions ($s = 1/2$),
containing a single, non-magnetic Zn$^{2+}$ impurity. Bond arrows
define site labels $i$ and $j$ in each interaction term $\mathbf{D} \cdot
\mathbf{s}_i \times \mathbf{s}_j$, while $\mathbf{D} = D \mathbf{e}_z$ with $D > 0$
for all bonds. Curving arrows denote the $\mathsf{C}_6$ symmetry about
the hexagon centers.}
\label{fig:system}
\end{figure}

This article is organized as follows. In Sec.~\ref{sec:model} we
introduce the model Hamiltonian and discuss some of the symmetry
aspects of the clusters considered in our exact-diagonalization
calculations. The results for the local magnetization response
are presented and analyzed in Sec.~\ref{sec:local}. In
Sec.~\ref{sec:correlations}, we investigate the dominant magnetic
correlations on the basis of the full correlation matrix (the ``natural
orbital'' method). We conclude in Sec.~\ref{sec:conclusions} with a
discussion of the implications of our results for experimental measurements
on ZnCu$_3$(OH)$_6$Cl$_2$. We also include two appendices which elaborate
on the magnetization response of a minimal (four-site) cluster
(App.~\ref{app:4sites}) and on the natural orbital method
(App.~\ref{app:Cij}).

\section{Model}\label{sec:model}

We consider a spin-1/2 model on the kagome lattice with a single,
non-magnetic impurity described by the Hamiltonian
\begin{equation}
\mathcal{H} = J \sum\limits_{\langle ij \rangle} \mathbf{s}_i \cdot \mathbf{s}_j
 + \sum\limits_{\langle ij \rangle} \mathbf{D}_{ij} \cdot \left( \mathbf{s}_i
\times \mathbf{s}_j \right) - \mathbf{B} \cdot \mathbf{S},
\label{eq:hamiltonian}
\end{equation}
with periodic boundary conditions. The first term is the Heisenberg
exchange energy between nearest-neighbor spins $\langle ij \rangle$, the
second term represents the DM interactions, and the last term
is the Zeeman energy of the total spin $\mathbf{S} = \sum_i \mathbf{s}_i$ in a
field $\mathbf{B}$. In what follows, we work in the fixed reference frame
$xyz$ shown in Fig.~\ref{fig:system}. The field is taken to be in the
$xz$-plane at an angle $\theta$ from the $z$-axis. The DM vectors on every
bond are taken to be perpendicular to the kagome plane and are fixed by the
symmetry of the clean system, namely translations and $\mathsf{C}_6$
rotations around the hexagon centers. We have chosen the site-labelling
convention, denoted in Fig.~\ref{fig:system} by the directionality of the
arrows from $i$ to $j$, such that $\mathbf{D}_{ij} = D\mathbf{e}_z$ with $D > 0$
for all bonds. In this study we do not consider an in-plane DM component,
because in ZnCu$_3$(OH)$_6$Cl$_2$ this is known\cite{Zorko} to be much
weaker than the out-of-plane component. We note, however, that the in-plane
DM problem on the kagome lattice is quite significantly different from its
out-of-plane counterpart studied here.\cite{Elhajal}

We will focus on the magnetization response of the system in finite
fields, up to the values $B \sim 10$ T ($B \lesssim J/20$) probed by
experiment. For a general field orientation $\theta$, the $\mathsf{U}(1)$
spin rotation symmetry around the $z$-axis is broken and thus the total
magnetization $S^z$ is not a good quantum number. Because of the impurity
site, the same is true also for the momentum. Thus we can treat kagome
clusters with a maximum of $N = 26$ magnetic sites, and here we show
primarily the results for $N=14, 20$, and $26$. These clusters are
symmetric with respect to spatial inversion through the impurity site.
For a non-degenerate ground state, this sets the constraints
\begin{equation}
\langle \mathbf{s}_1\rangle=\langle \mathbf{s}_{8}\rangle, ~\langle \mathbf{s}_2
\rangle=\langle \mathbf{s}_{7}\rangle,~\langle \mathbf{s}_3\rangle=\langle
\mathbf{s}_{12}\rangle,~\dots
\end{equation}
Furthermore, the clusters with $N = 14$ and $26$ are also spatially
symmetric under reflection through the $xz$-plane which passes through
the impurity site (Fig.~\ref{fig:system}), whence their Hamiltonian
(\ref{eq:hamiltonian}) remains invariant under the corresponding mirror
operation (spatial reflection followed by the time reversal). For a
non-degenerate ground state, this gives in addition
\begin{eqnarray}
\langle s_1^{x,z}\rangle &=& \langle s_{7}^{x,z}\rangle,~\langle s_1^y
\rangle = -\langle s_{7}^y\rangle \nonumber\\
\langle s_2^{x,z}\rangle &=& \langle s_{8}^{x,z}\rangle,~\langle s_2^y
\rangle = -\langle s_{8}^y\rangle,~\dots
\label{eq:symm2}
\end{eqnarray}
This mirror symmetry is also present in the clean, infinite kagome
lattice. Thus if the vacant site were occupied by a spin $\mathbf{s}_0$,
Eq.~(\ref{eq:symm2}) would require $\langle s_0^y \rangle = 0$.
The remaining symmetries of the clean kagome lattice would then enforce
$\langle s_i^y \rangle = 0$ for all sites $i$, an argument we will employ
below to demonstrate that in the disordered phase ($D/J\lesssim 0.1$)
there can be no staggered magnetic response along the $y$-axis sufficiently
far from a vacant site.

\begin{figure}[!t]
\includegraphics[width=0.45\textwidth]{Profiles_Kag26_B0p05_theta30}
\caption{(Color online) In-plane magnetizations and bond spin correlation
functions for the 26-site kagome cluster with $B = J/20$ and $\theta =
30^\circ$. The lengths of the arrows are proportional to $\left( \langle
s_i^x \rangle^2 + \langle s_i^y \rangle^2 \right)^{1/2}$ and the
thicknesses of the bonds to $\langle \mathbf{s}_i \cdot \mathbf{s}_j \rangle$.}
\label{fig:profiles}
\end{figure}

In addition to these ``symmetric'' clusters, we have also investigated
clusters with odd numbers of magnetic sites, particularly with $N = 17$
and $23$, whose ground state has a finite moment $S_z = 1/2$. As shown
in Ref.~[\onlinecite{Didier}], this moment does not form a bound state
around the impurity site, as is the case in systems such as the
checkerboard lattice,\cite{Didier} but is delocalized over the entire
cluster. Thus we expect no difference between clusters with even or odd
numbers $N$ of magnetic sites in the thermodynamic limit, and our results
indeed conform with this picture.

\section{Local response}\label{sec:local}

Figure \ref{fig:profiles} shows the local in-plane magnetizations $\langle
s_i^{x,y} \rangle$ (red arrows) and the local spin correlation functions
$\langle \mathbf{s}_i \cdot \mathbf{s}_j\rangle$ (described quantitatively by
the thickness of each bond $ij$) for the 26-site cluster with $B = J/20$,
$\theta = 30^\circ$, and for four representative values of $D/J$. The
full $D/J$-dependence of the in-plane magnetizations, the correlation
amplitudes, and the local twist amplitudes $\langle (\mathbf{s}_i \times
\mathbf{s}_j)^z\rangle$ is shown for each type of site or bond in
Fig.~\ref{fig:all26sites}. These results demonstrate that there exist
two primary regimes with qualitatively different magnetic response,
whose properties we discuss in detail in the following subsections. In
summary, these are (i) the small-$D/J$ regime ($D/J\lesssim 0.06$), where
there is a local, dimer-like response for the sites around the impurity,
and (ii) the large-$D/J$ regime ($D/J\gtrsim 0.1$), which is characterized
by the expected\cite{Elhajal,Ballou,Cepas} in-plane, 120$^\circ$ magnetic
ordering pattern, albeit with a special response from the sites right next
to the vacancy. We also find an apparent intermediate regime ($0.06
\lesssim D/J \lesssim 0.1$) with a peculiar magnetization pattern around
the impurity, but with no evidence of long-ranged magnetic correlations,
and we will also characterize this to the extent that our calculations allow.

\begin{figure}[!t]
\includegraphics[width=0.48\textwidth]{DMdependence_Kag26_B0p05_theta30_v2}
\caption{(Color online) $D$-dependence of (a) $\langle s_i^x \rangle$,
(b) $\langle s_i^y \rangle$, (c) $\langle \mathbf{s}_i \cdot \mathbf{s}_j \rangle$,
and (d) $\langle \mathbf{s}_i \times \mathbf{s}_j \rangle^z$ for the 26-site kagome
cluster with $B = J/20$ and $\theta = 30^\circ$. $i$ and $j$ in panels (c)
and (d) are nearest-neighbor sites only. The curves which correspond to the
sites or bonds closest to the impurity are designated by (red) filled symbols.}
\label{fig:all26sites}
\end{figure}

\subsection{$D \lesssim 0.06J$: local dimer-like response}

We begin by considering the behavior of the nearest-neighbor spin
correlations, $\langle \mathbf{s}_i \cdot \mathbf{s}_j\rangle$, which are shown
in Fig.~\ref{fig:all26sites}(c) and are also denoted by the bond thicknesses
in Fig.~\ref{fig:profiles}. A low-$D$ regime, where the correlations
are controlled by the exchange interaction ($J$) and by the presence of the
impurity, can be seen to exist for $D/J \lesssim 0.06$, although in fact
the correlation amplitudes begin to deviate from their zero-$D$ limit at
$D/J \sim 0.03$. This limit was studied in detail
in Ref.~[\onlinecite{Dommange}] and is characterized by a large and
oscillatory variation of the correlation amplitudes as a function of
distance from the impurity. As shown in Fig.~\ref{fig:profiles}(a), the
strongest dimerization is found on the bonds nearest the vacancy, where
$\langle \mathbf{s}_i \cdot \mathbf{s}_j \rangle \simeq -0.69$ is very close to
the value of $-0.75$ expected for an isolated dimer. This local ``dimer
freezing'' is a key consequence of the frustration relief in the two
triangles containing the vacancy\cite{Dommange,Lauchli} and, as we will
discuss below, has direct implications for the magnetization response of
the corresponding sites in the small-$D/J$ regime.

The local twist amplitudes $\langle (\mathbf{s}_i \times \mathbf{s}_j)^z
\rangle$ shown in Fig.~\ref{fig:all26sites}(d) represent, from
Eq.~(\ref{eq:hamiltonian}), the DM contribution to the total magnetic
energy. As expected for the small $D/J$ regime, these scale linearly
with $D/J$ for all bonds, although with a quite inhomogeneous distribution
of slopes depending on the distance of the bond from the impurity. In
particular, the bonds closest to the impurity have one of the smallest
twist amplitudes, as might be anticipated from their strong dimerization.

Turning next to the magnetization response shown in
Figs.~\ref{fig:profiles}(a) and \ref{fig:all26sites}(a)-(b), this develops
predominantly in the $xy$-plane, as expected given the easy-plane character
of the DM anisotropy, and the induced spin components are of order
$\langle s_i^{x,y} \rangle \sim 10^{-3}$--$10^{-2}$. By contrast, the
out-of-plane response is very small ($\langle s_i^z \rangle \lesssim
10^{-6}$), and thus will not be considered in the following. With the
exception of sites strongly influenced by the periodic boundary conditions,
the magnetization response shows a number of features which are also present
in the 20-site cluster and can be understood qualitatively on the basis of
the strong local dimer formation around the impurity. Indeed, the direction
of the induced magnetizations at the strongly dimerized bonds is qualitatively
similar to the response expected\cite{Miyahara} if they were isolated: a
staggered polarization in the direction $\mathbf{D} \times \mathbf{B}$ (here the
$y$-axis) and a uniform polarization in the direction $(\mathbf{D} \times
\mathbf{B}) \times \mathbf{D}$ ($x$-axis). At the quantitative level, the actual
magnitude of the magnetization response goes beyond the isolated-dimer
picture, showing the striking feature that the moments induced on the four
``next-most-strongly'' dimerized bonds [bond (3,4) and its equivalents in
Fig.~\ref{fig:system}] are larger by a factor of 3-4 than on the bonds
closest to the impurity. The origin of this result, which we probe in
detail below, is rather deeper than a simple anticorrelation between
spin correlation amplitude and induced moment. It lies in the fact that,
while the ground-state wave function close to the impurity can be described
as an approximate product state of local dimers, the actual nature of the
excitations may nevertheless differ significantly from such a picture.

\begin{figure}[!t]
\includegraphics[width=0.4\textwidth]{ProfilesTwoTriangles_B0p05_theta30}
\caption{(Color online) In-plane magnetization pattern (red arrows) and
bond strengths (bond thickness in blue) on the isolated six-site cluster
discussed in Sec.~\ref{sec:local}, for $B=J/20$ and $\theta=30^\circ$.}
\label{fig:6sites}
\end{figure}

To clarify this point, we isolate the sites 1-6 of Fig.~\ref{fig:system}
and consider their response in the small-$D/J$ regime. Figure \ref{fig:6sites}
shows the exact magnetization response of this cluster with parameters $B =
J/20$, $\theta = 30^\circ$, and for the same field orientation and four
representative values of $D/J$ shown in Fig.~\ref{fig:profiles}. The
response for $D = 0.05J$ is very similar to that of the sites 1-6 in
Fig.~\ref{fig:profiles}, and in fact the same physics can also be
shown to dominate the response of a four-site cluster (sites 1-4 of
Fig.~\ref{fig:system}), as detailed in App.~\ref{app:4sites}. In all
cases, the magnetizations induced on bond (3,4) are larger than those on
bond (1,2) by a fixed factor of up to 5. The qualitative interpretation
(App.~\ref{app:4sites}) of this result lies in the different character
of the local excitations on bonds (1,2) and (3,4): a triplet excitation
on bond (1,2) is a true eigenstate of the isotropic Hamiltonian, whereas
a similar triplet excited on the bond (3,4) is not, and may propagate away.
As a result, the magnetization response of bond (1,2) is to first order in
$D/J$ the same as that of an isolated dimer, while that of bond (3,4)
will be almost 5 times larger in the extreme case of the four-site
cluster. The same arguments apply not only on the six-site cluster, but
also to the impure kagome lattice, although in this latter case a triplet
excitation on the bonds next to the impurity does not remain fully
localized because the bonds are not fully ``frozen.'' More generally,
the qualitative agreement between the response of the smallest clusters
and the response of the corresponding sites in the $20$ and $26$-site
calculations shows that, in the regime of small $D/J$, the magnetization
profile around the impurity is governed almost entirely by local correlations.

The magnetization response far from the impurity is expected to be that
of the clean kagome lattice with DM interactions. As explained above, the
staggered magnetization must vanish by symmetry, while a uniform component
(along the $x$-axis) can survive. This latter scales as $\mathbf{D} \times
(\mathbf{D} \times \mathbf{B})$ (see also Ref.~[\onlinecite{Tovar}]) and thus
is very much weaker than the staggered response in close proximity to the
impurity. This result is corroborated by exact-diagonalization calculations
on a clean, 12-site kagome cluster (not shown here), which reveal a very
weak uniform response ($\langle s_i^x \rangle \sim 10^{-7}$). We comment
that results for larger clean clusters ($N = $18 and 24) suffer from severe
finite-size effects due to the presence of inequivalent loops in these
geometries, and thus cannot be used for a quantitative determination
of the magnetization response far from the impurity in the thermodynamic
limit.

\subsection{$D \gtrsim 0.1J$: semiclassical, $Q=0$, $120^\circ$ ordered state}

At large values of $D/J$ [Fig.~\ref{fig:profiles}(d)], the magnetization
profiles correspond closely to the expected\cite{Elhajal,Ballou,Cepas}
$Q = 0$, semiclassical, three-sublattice (120$^\circ$) state. We note
here that in this case the magnetic field and the impurity combine to
pin one of the (infinitely many) degenerate semiclassical states. This
can be understood physically from the fact that the selected configuration
is the one in which the spin missing at the impurity site would be
antiparallel to the field, and thus would contribute a positive Zeeman
energy. However, Fig.~\ref{fig:profiles}(d) also shows that the spins
closest to the impurity are slightly tilted away from a perfect 120$^\circ$
orientation. In fact these spins do not participate in the ordered state in
the same way as all the other (``bulk'') spins do, as can be inferred from
the spin correlation amplitudes in Fig.~\ref{fig:all26sites}(c). Above
$D/J \sim 0.06$, and especially beyond $D/J \sim 0.6$, all the bonds except
the two closest to the impurity attain very similar strengths. By contrast,
the dimers next to the impurity (denoted by filled symbols) resist this
tendency, their spins remaining strongly correlated up to surprisingly
high values in excess of $D\sim J$. There is no such feature on the
neighboring bonds, i.e.~there is no indication of a length scale in this
behavior. This is another primary consequence of frustration relief on
the triangles hosting the impurity, and will be further corroborated by
our analysis of the in-plane correlation data in Sec.~\ref{sec:correlations}.

One further comment regarding the behavior of the twist amplitude at large
$D/J$ is in order here. In the clean kagome system, the twist amplitude is
the same on every bond, but according to Fig.~\ref{fig:all26sites}(d), the
sites next to the impurity have a twist amplitude, $\langle( \mathbf{s} \times
\mathbf{s}_j)^z \rangle \simeq -0.3$ for $D/J \to \infty$, larger than on any
of the other bonds. This reflects the fact that the relative orientation of
these two spin pairs lies between the 120$^\circ$ orientation of the spins
on triangles and the 90$^\circ$ orientation favored in an isolated dimer,
and as such shows the consequence of frustration relief for the DM interaction.

\subsection{Intermediate regime: $0.06\lesssim D/J\lesssim 0.1$}

Our results for the local magnetic properties (Figs.~\ref{fig:profiles} and
\ref{fig:all26sites}) imply the presence of an intermediate regime, $0.06
\lesssim D/J \lesssim 0.1$, which cannot be classed as being in either of
the above limits. Here the spins develop a peculiar magnetization pattern
around the impurity site, seemingly indicative of spins with no effective
interaction which only follow the applied field. This is shown for the case
$D/J = 0.1$ in Fig.~\ref{fig:profiles}(c), but the analogous picture for
$D/J = 0.07$ is practically indistinguishable. We have investigated
this regime in considerable detail as a function of $D/J$, of the applied
field $B/J$, and of the field angle $\theta$, finding essentially perfect
linear response to the field down to the lowest energy scales. As we will
show in Sec.~\ref{sec:correlations}, the in-plane magnetic correlation data
show no evidence for long-ranged magnetic order in this regime.

While we cannot exclude the possibility of some type of exotic order in
this regime, such as a chiral or a spin-nematic phase, we are unable to
find any evidence of a local order parameter. Thus we feel that, pending
further studies by other approaches, the most likely explanation for the
peculiar magnetization patterns we observe lies in finite-size effects.
One of the reasons that these effects are strong here is the fact that
a uniform magnetic field is not the appropriate conjugate field for the
three-sublattice ordered state, and thus competes with this type of order
close to the critical point where the size of the ordered moment is small.

\section{Magnetic correlations}\label{sec:correlations}

Although the analysis of the local magnetization data in Sec.~III
reveals several major, qualitative features of the ground state of
Eq.~(\ref{eq:hamiltonian}), a number of issues remain unresolved.
One is whether there exists any type of magnetic order in the window
$0.06 \lesssim D/J \lesssim 0.1$, and what is the actual critical value
of $D/J$ where the 120$^\circ$ phase is established. Another concerns the
fact that the magnetization patterns shown in Fig.~\ref{fig:profiles} give
few indications regarding the consequences of finite-size effects in our
calculations, which may be quite different in different parameter regimes,
and a method is required by which to make this more systematic. Further,
the actual magnitudes of the moments in the ordered phase cannot be
inferred from the local magnetization data, because the latter do not
represent the thermodynamic limit. While we will obtain these
moments, here we will not pursue the observation, from our numerical data
for the field-dependence of the magnetizations at large $D$ ($D/J \gtrsim 1$),
that a very large field ($B/J \sim 1$) is required to establish their full
lengths.\cite{Capponi}

It is thus necessary to analyze the magnetic correlations in the ground
state $|\Psi\rangle$ of Eq.~(\ref{eq:hamiltonian}) as a function of $D/J$.
The easy-plane character of the DM anisotropy allows us to focus on
in-plane correlations, but the breaking of translational invariance by
the impurity makes it necessary to consider the full set of these, which
is contained in an $N \times N$ matrix with entries
\begin{equation}\label{eq:Cij}
C_{ij} = \langle \Psi| s_i^+s_j^-|\Psi\rangle.
\end{equation}
We remark here that an analysis based on the connected (or cumulant)
correlation matrix instead of on $\mathbf{C}$ (\ref{eq:Cij}) gives the same
results because, for the fields considered in this study, the local
magnetic moments $\langle s_i^{\pm} \rangle$ are negligibly small compared
to the connected portion of the correlations, a result which is true for
both small and large values of $D/J$. A further consequence of this
is that our low-field correlation data ($B = J/20$ in the calculations to
follow) are essentially identical to the $B = 0$ case.

For translationally invariant systems, the correlation matrix can be
partially or fully diagonalized by a simple Fourier transformation.
In the present case, where translational invariance is absent due to the
non-magnetic impurity, $\mathbf{C}$ must be diagonalized numerically.
The information contained in $\mathbf{C}$ is very useful, especially if the
ground state contains long-ranged magnetic correlations in the $xy$-plane.
In this case, it is known (Refs.~[\onlinecite{Penrose,Yang}] and
App.~\ref{app:Cij}) that the maximum eigenvalue $\lambda_m$ of $\mathbf{C}$
is macroscopically large, i.e.~$\lambda_m \propto N$. The corresponding
eigenvector, $\boldsymbol{v}_m$, then describes the magnetic mode of the system
with the dominant fluctuations, and thus is related directly to the spatial
dependence of the relevant order parameter. In the case at hand, the
dominant mode $\boldsymbol{v}_m$ is not simply a periodic modulation of the spins,
but will contain valuable information for the non-trivial magnetization
profile around the impurity. In what follows we exploit this information.

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{CorrelationsEvals_Kag1417202326_B0p05_theta30_2}
\caption{(Color online) Eigenvalues $\lambda_i$ of the correlation matrix
(divided by $N$) as a function of $D/J$ for $N = $14 (circles), 17 (down
triangles), 20 (squares), 23 (up triangles), and 26 (diamonds). Here $B =
J/20$ and $\theta=30^\circ$, but the results for $B = 0$ are identical.}
\label{fig:Cevals}
\end{figure}

\begin{figure}[t]
\includegraphics[width=0.45\textwidth]{lambdaScaling3}
\caption{(Color online) Scaling with system size of the largest eigenvalue
$\lambda_m$ (divided by $N$) of the correlation matrix. The solid lines
correspond to the expected $1/\sqrt{N}$ scaling of the leading corrections
to the thermodynamic limit in the 120$^\circ$ ordered phase.}
\label{fig:scaling}
\end{figure}

Figure \ref{fig:Cevals} shows the full eigenvalue spectrum of $\mathbf{C}$
for clusters with N$=$14, 17, 20, 23, and 26. The results for $B = 0$ and
$B = J/20$ are indistinguishable. An essential feature of Fig.~\ref{fig:Cevals} is
that, as $D/J$ is increased in the region beyond $0.06$, the maximum
eigenvalue on each of the clusters becomes proportional to $N$, and thus
very much larger than the remaining eigenvalues; we caution that the
actual value of this crossover cannot be inferred from the data of
Fig.~\ref{fig:Cevals}, where it is evident that the curves are still
some way from the thermodynamic limit, and address this point below. As
described in App.~\ref{app:Cij}, this means that the system has developed
long-ranged in-plane magnetic correlations in the regime of large $D/J$.
For small $D/J$, all the eigenvalues depend only weakly on $D/J$ and are
closely spaced in magnitude, which is a sign of short-range correlations
dictated not by $D$ but by $J$.

The finite-size scaling of the dominant eigenvalue $\lambda_m$, normalized
by $N$, is given in Fig.~\ref{fig:scaling}. The extrapolated values of
this quantity represent the square of the average magnetic moment in the
thermodynamic limit, where the spins reach approximately $80\%$ of
their full moment as $D/J\to \infty$.\cite{factor2} For all values $D/J
 > 0.1$, it is clear that the finite-size corrections scale as $1/\sqrt{N}$,
as expected for a state of broken U(1) symmetry.\cite{scaling} This scaling
procedure represents the appropriate means of deducing the existence of
long-ranged magnetic order, by continuing the curves of Fig.~\ref{fig:Cevals}
to the infinite-system limit. However, this powerful method shows no
indication of such order in the regime $0.06 \lesssim D/J \lesssim 0.1$,
specifying that the transition to the semiclassical state should be taken
as $D/J \simeq 0.1$.

The magnetization profile corresponding to the dominant eigenmode
$\boldsymbol{v}_m$ also contains important information, which is shown in
Fig.~\ref{fig:CorrDomMode} for the four representative values of $D/J$ and
represented by two-dimensional arrows whose components are the real and
imaginary parts of $\boldsymbol{v}_m$. At $D/J\lesssim 0.06$, there is no dominant
mode as is the case at large $D$, but the strongest mode shown in
Fig.~\ref{fig:CorrDomMode}(a) corresponds nevertheless to the pattern of
strong spin correlations around the impurity [Fig.~\ref{fig:profiles}(a)]:
the correlations in this mode are confined to the strong bonds next to the
impurity, where the spins are almost antiparallel. The strength of these
local correlations is governed by $J$, which is the reason why $\lambda_m$
remains essentially $D$-independent for $D/J\lesssim 0.06$ in
Fig.~\ref{fig:Cevals}. We emphasize again that the profile shown in
Fig.~\ref{fig:CorrDomMode}(a) does not represent the actual magnetization
response -- this is shown in Fig.~\ref{fig:profiles}(a) -- but rather the
dominant fluctuation mode.

\begin{figure}[!b]
\includegraphics[width=0.5\textwidth]{CorrelationsDomMode_Kag26_B0_SeveralD}
\caption{(Color online) Magnetization profile for the 26-site kagome cluster
in zero field, corresponding to the eigenvector $\boldsymbol{v}_m$ of $\mathbf{C}$ with
the largest eigenvalue $\lambda_m$. The in-plane moments are given by the
real and imaginary parts of $\boldsymbol{v}_m$. Note that this mode is unique up to
a global U(1) rotation which is related to the arbitrary phase of $\boldsymbol{v}_m$.}
\label{fig:CorrDomMode}
\end{figure}

\begin{figure}[!t]
\includegraphics[width=0.48\textwidth]{AnglesAndSpinLengthsFromCorrelations}
\caption{(Color online) In-plane spin magnitudes and orientations
(represented respectively by $\sqrt{\lambda_m} |\boldsymbol{v}_m(i)|$ and by the
phase $\theta_i$ of $\boldsymbol{v}_m(i)$) as a function of $D/J$, for clusters
with $N = 14$ (circles), $20$ (squares), and $26$ (triangles). The data
corresponding to the four sites closest to the impurity are highlighted
by filled symbols.}
\label{fig:SpinLength}
\end{figure}

The situation changes dramatically at $D/J \gtrsim 0.1$
[Figs.~\ref{fig:CorrDomMode}(c)-(d)], where the system develops
long-ranged order with the majority of spins participating in the
$Q = 0$, semiclassical 120$^\circ$ state. The data show clearly that the
crossover from the dimer-like regime at small $D/J$ to the ordered phase
at high $D/J$ is smooth, and there are no indications for any other type
of magnetic order in the intermediate regime $0.06 \lesssim D/J \lesssim 0.1$.
This suggests once again that the peculiar magnetization pattern found in
Fig.~\ref{fig:profiles}(b) is most likely to be a fluctuation effect which
is emphasized close to the critical point.

Indeed, our analysis of the magnetic correlations allows us to develop
a qualitative understanding of the situation in this regime. The kagome
AFM is characterized by a very high density of nearly-degenerate states
in the ground manifold. The effect of a DM interaction term $D$ is to
favor certain states and penalize others, but this process is extremely
sensitive to the shape and size of the cluster used in the calculations.
Some of our results, such as the discrepancy between Figs.~\ref{fig:profiles}(c) and
\ref{fig:CorrDomMode}(c), are evidence of significant finite-size effects.
These effects are expected to, and indeed in
Figs.~\ref{fig:Cevals} and \ref{fig:scaling} observed to, increase on
approaching the critical regime around $D/J \sim 0.1$. With such small
separations between sets of energy levels, the effect of a magnetic field
applied in this regime can be dramatic: certainly some of the differences
between Figs.~\ref{fig:profiles} and \ref{fig:CorrDomMode} may be
ascribed to the finite field in the former. While it remains impossible
to exclude more exotic types of order for $0.06 \lesssim D/J \lesssim 0.1$,
whose fingerprints might be difficult or even impossible to discern in
data obtained from the cluster sizes accessible by exact diagonalization,
these considerations make systematic our statement that the most probable
explanation for the tendency of the small-$D/J$ and large-$D/J$ data to
suggest the presence of an intermediate regime remains in the realm of
finite-size effects.

The magnetic correlation data also quantify the extent to which the
four sites closest to the impurity continue to resist the effect of $D$
(Fig.~\ref{fig:CorrDomMode}). As already inferred from the behavior of
the correlation amplitudes (Fig.~\ref{fig:profiles}), these spins do not
adopt a relative 120$^\circ$ orientation, but remain almost antiparallel
to each other up to DM interactions $D \sim J$. This direct consequence
of frustration relief in the two doped triangles also suggests that the
actual orientation of the ordered component of these spins will continue
to reflect the behavior of a dimer, and thus will be dictated by $\mathbf{D}$
and $\mathbf{B}$ as well as by the coupling to the other spins. Only at
surprisingly high values of $D/J$ does a crossover occur to predominant
correlation with the other spins of the system, and hence to participation
in the 120$^\circ$ ordered state.

This special response of the four sites closest to the impurity is
demonstrated once again in Fig.~\ref{fig:SpinLength}, which shows the
orientation and magnitude of the spin components obtained from
the dominant eigenmode $\boldsymbol{v}_m$. Here the spin magnitude at site $i$ is
represented by $\sqrt{\lambda_m} |\boldsymbol{v}_m(i)|$, while the corresponding
angle is determined from the phase representation of the real and imaginary
parts of $\boldsymbol{v}_m(i)$. The primary feature of Fig.~\ref{fig:SpinLength} is
that, while both the magnitude and the orientation for the majority of sites
(open symbols) largely merge together at $D/J \gtrsim 0.06$, the same
quantities for the four sites closest to the impurity (filled symbols)
remain different up to $D \sim J$. This feature, present in all three
clusters, reinforces the picture of the special behavior of the
frustration-relieved spins.

\section{Summary and discussion}\label{sec:conclusions}

We have presented an extensive exact-diagonalization study of the
combined effects of non-magnetic impurities and Dzyaloshinskii-Moriya
(DM) interactions in the $s = 1/2$ kagome antiferromagnet (AFM). Although
the clean and purely Heisenberg kagome AFM remains an enigma, being
apparently non-magnetic and possibly dimer-based, we have shown how
DM interactions immediately induce a magnetic response, and impurities
immediately nucleate very strong and somewhat extended patterns of
dimerization. We have found that the system undergoes a phase transition
from this magnetically disordered state to the $Q = 0$, three-sublattice
(120$^\circ$) ordered state when the interaction ratio between the DM and
AFM terms is $D/J \sim 0.1$. This conclusion is in agreement with the
results obtained by C\'epas {\it et al.} for the clean kagome
lattice.\cite{Cepas}

For $D/J\lesssim 0.06$, there is strong dimerization of the spins next to
each impurity site as a consequence of frustration relief in these two
triangles, as shown by Dommange {\it et al.}\cite{Dommange} for the $D = 0$
case. An oscillating pattern of weakly and strongly dimerized bonds then
extends some distance from the impurity site. In the presence of DM
interactions, the applied field induces a magnetic response on top of
this dimerization pattern, which on the strongly dimerized bonds shows
the same qualitative behavior as an isolated dimer, namely a dominant
staggered component directed along $\mathbf{D} \times \mathbf{B}$. The induced
magnetic moments on the sites closest to the vacancy are small as a result
of their strong dimerization, and we have shown why the magnetization on
the next-nearest strong bonds is approximately four times larger than this.
The maximum induced magnetization is thought to occur on these sites or on
the next (i.e.~next-next-nearest) ``ring'' of more strongly dimerized
bonds beyond them.\cite{Dommange} Still further from the impurity, the
local moment decreases again, towards the weak and uniform response
(by which is meant no staggered component) of the clean kagome system with
DM interactions. Because this is proportional to $\mathbf{D} \times (\mathbf{D}
\times \mathbf{B})$, it is much smaller than the staggered response around
the impurity sites.

The ordered phase established at $D/J \gtrsim 0.1$ shows all the hallmarks
expected for semiclassical magnetic order. However, we found that the
spins closest to the impurity remain strongly correlated with each other
up to surprisingly large values, $D \sim J$, before they begin to
participate fully in the ordered state. Thus a substantial portion of
the actual magnetization of these spins remains similar to that of a
dimer, and is set by $\mathbf{D}$ and $\mathbf{B}$. Despite the fact that the
obvious features of these two phases end at separate values of $D/J$ which
leave open the possibility of an intermediate phase, between these limits
we have been unable to find any definite evidence for another type of
physical behavior. Thus we are forced to the tentative conclusion that
there is only one true phase transition in the system, and the features
we have observed for $0.06 < D/J < 0.1$ are most likely to be artifacts
resulting from the low effective energy scales in this regime and from
the small system sizes to which our calculations are constrained.

We conclude by discussing the implications of our results for the
interpretation of experiments performed on ZnCu$_3$(OH)$_6$Cl$_2$.
The most accurate probe of the local magnetic response around doped
impurities is NMR, and so we focus on the $^{17}$O NMR measurements
of Olariu {\it et al.}\cite{Olariu} Before comparing the experimental
results to our calculations, which were performed for a single vacancy
in small kagome clusters, it is necessary to consider the impurity
concentrations in the experimental samples. Because these are on the
order of 5\% for the cleaner samples used in the measurements made to
date,\cite{Olariu} the average linear spacing between impurities is then
4-5 Cu--Cu bond spacings: in fact this is rather similar to the lengthscales
probed in our $N = 20$ and 26 clusters. From our results, it is safe
to say that there are no Cu spins in the real material which can be
considered as being far from any impurity sites.

Our conclusions show that the situation $D/J > 0.1$ may be safely excluded
for herbertsmithite, because a magnetically ordered phase of any type is
inconsistent not only with the NMR experiments but also with muon spectroscopy
and inelastic neutron scattering experiments,\cite{muons,Helton} where no
such order has been found for any temperatures down to 50 mK. By contrast,
for DM interactions $D/J < 0.1$, one would expect to observe a broad NMR
signal as a consequence of the considerable number of inequivalent Cu sites
produced by the partially frozen patterns of dimerization and induced local
moments around the randomly distributed impurities. This is compatible
with the shape of the (M) line measured in Ref.~[\onlinecite{Olariu}], while
the (D) line, which probes only one type of Cu site, would indeed be expected
to be sharp. Further, our calculations quantify the way in which the DM
interaction removes the apparent singlet nature of the $D = 0$ ground state,
leading to the finite lineshift observed in experiment in the limit $T \to 0$.

To be more specific about the actual strength of $D/J$ in herbertsmithite
within the disordered regime, we appeal to our results (Sec.~III) for the relative local moments on
the sites around an impurity. On the qualitative assumption that the $^{17}$O
line shift should scale with the sum of the moments on the two neighboring
Cu sites, the 1:4 moment ratio found for the nearest two Cu sites in the
low-$D$ regime ($D/J \lesssim 0.06$) would be expected to result in a 1:5
ratio of line shifts. Thus the observed 1:2 ratio\cite{Olariu} suggests
quite strongly that herbertsmithite falls in the regime $0.06 \lesssim D/J
\lesssim 0.1$ while the exact nature of the ground state in this region
remains to be confirmed, it is clear that it is non-magnetic, and that the
moment ratio between the two types of Cu sites closest to an impurity is
significantly smaller than at low $D/J$ [Fig.~\ref{fig:SpinLength}(b)]. Such
a value for $D/J$ is fully consistent with the result $D \simeq 0.08J$
obtained by electron spin resonance in Ref.~[\onlinecite{Zorko}].

Finally, we have shown in the disordered regime ($D/J \lesssim 0.1$) that
sites close to the impurities exhibit strong features characteristic of the
response of isolated dimers, with those right next to an impurity (the (D)
line) reflecting a very weak induced magnetization. This behavior could
explain the suppressed local susceptibility at $T \to 0$ and the enhanced
spin-relaxation times $T_1$ found\cite{Olariu} for these sites. However,
to go beyond this qualitative level of agreement, it seems necessary to
have access to single-crystal data, which would provide a detailed
understanding of the hyperfine interactions in ZnCu$_3$(OH)$_6$Cl$_2$.
These are required to investigate the dependence of the magnetic response
on the field orientation and the line-shift contributions from each Cu
site as a function of its induced magnetization, information which could
be interpreted directly within our calculational approach.

\section{Acknowledgments}
We are grateful to O. C\'epas, C. Lhuillier, P. Mendels, and A. Olariu
for fruitful discussions. This work was supported by the Swiss National
Science Foundation and by MaNEP.

redpajama_set_name: RedPajamaArXiv


If your complexion and skin color is slightly beige then it is likely you will have olive skin. Olive skin allows you to look good in warm, summary colors like yellow and orange. Olive skin is also great for hiding those blemishes that you do not want people to see.
Olive skin is found in many people from different ethic backgrounds but is usually found in Europeans rather than the British such as in Spain and Italy, in the Mediterranean.
People who have this type of skin can have hair from dark blond to black hair and can have brown, green or blue eyes.
People consider olive skin to be more beautiful and more appealing than that of pale skin.
This is an example of why British tourists go on holiday, in order to gain a tan.
People also perceive an olive tan to be healthier and healthier looking; when in fact it is not because exposure to sunlight causes the skin to age, dry and even expose you to getting sun cancer.
People with olive skin though may feel that because they tan easily they are not as much at threat to skin cancer than that of someone with a pale looking skin tone. This is not the case though.
It just means that they have more melanin which protects you better from more harmful rays.
Having olive skin also means you are less likely to have or get dry skin in comparison to very fair skinned people.
This due to you having slightly larger pores in the skin. Olive skin tends to mean that you age well and do not have or receive as many wrinkles as that of fair skinned people.
In saying this you are more prone to the skin sagging and the wrinkles you do get will be deeper.
The sagging is due to you having thicker sub cutis and dermis.
If you don't have olive skin then there are many products available in the shops that allow you to get that natural olive look.
It can be found out of a bottle and are creams that gradually build up the color of your skin. Unlike fake tan it only gradually builds up a natural looking color rather than a deep bronzer.


text:
Pickwick: 'Lying Awake In The Dark' [Song Premiere]
The ever-restless Seattle standouts return with their strong, slinky sophomore record after four years wait. Listen to a new track from 'LoveJoys' now and then leave a comment below to win tickets to their Doug Fir show on June 24.
Doug Fir Lounge
Photo by Ellie LillstromPickwick aren't a band who are easily satiated. In the early days, the burgeoning group were yet another Wilco-derivative, alt country act from Seattle. Their sound was mediocre and no one came to the shows.
When they stopped caring about genre, it led to a stellar record of soul-injected pop, 2013's Can't Talk Medicine. And although that record, coupled with their intense, sweaty live performances, won the band many fans, they've since stripped the tracks and the well-received demos that preceded its release from their Bandcamp page.
It seems they just weren't content with the sounds of their low-fi soul and R&B. In fact, in the years between that debut and the impending LoveJoys—due out July 7—they recorded and discard a lot of, in their opinion, terrible music (including some 40 songs for a pop R&B record).
After four long years, Pickwick's sophomore record 'LoveJoys' will be released on July 7 via Small Press RecordsSo, they went back to the basement where it all began and realized that all they really had to do was focus on having a good time.
"We rediscovered what we do best by not overthinking what we make, and learned to love the process of creating again," vocalist Galen Disston explains. And "that's precisely when the sounds started pouring out. We got out of each other's way and each individual member was able to contribute what we each do best without obstruction or worry. We worked together, but this time it was to a more cohesive end without compromising what we each value as musicians."
Prince had recently passed so they delved into his sonic legacy and found a funkier sound. Plus, it helped that guitar player Michael Parker won the Washington State Lottery and bought himself some toys.
"It felt great, after years of self-imposed stagnation, we were able to enter in to the uncertain territory of submitting oneself to the process of writing a song," Disston continues. "It's a rare and scary thing; songwriting requires fully engaging in a process that is fluid and never identical. It's a science of continually entering into something unknown. And it's an incredible feeling when a song appears. It's fun."
After months of writing, Disston, Parker, keyboard player Cassady Lillstrom, bassist Garrett Parker, and drummer Alex Westcoat took their efforts to producer Erik Blood, known for his work with Shabazz Palaces, Tacocat and The Moondoggies. Blood picked things apart and "pushed us into a new and better sound," Disston says.
"'Lying Awake In The Dark' was the last song written before we went into the studio to record LoveJoys," Disston tells. "It was written the day before I believe, and I think it was only three of us messing with it. We had the skeleton of the three different parts including the ahhh part, which I love because it's perhaps the only part of the record where I hear our adoration of Tropicália seeping in."
Pickwick's Galen Disston at the Doug Fir Lounge in 2014—click to see more photos by Josh PhillipsRecorded at Blood's Black Space Labs (his home studio) and Chemical X Studios (located in the basement of The Old Rainier Brewery building in industrial SoDo) in February 2016, Blood shares his studio with Ishmael Butler of Shabazz Palaces "and he brought in Alina To who I was familiar with from Grand Hallway [and also of Passenger String Quartet] to do the strings," Disston details. "The string parts, which were Blood's brainchild, really gave the song a '70s orchestral identity that I dig after devoting myself to Marvin Gaye's 'What's Going On.' It was cool to be a part of such an amorphous idea of a song that became so substantial after strings were added. Then we recorded an octave of my vocals to try to further ground the trippy song, and then we had something that felt good to listen to when driving a long drive at night. That's when you know you have something."
As illustrated by the above process, Pickwick are not a band to repeat themselves. Resting on their laurels is simply not satisfactory—and not even remotely satisfying.
Case in point: "We've written most of the songs for the next record and I'm looking forward to making another record with Blood," Disston reveals. "It's where my head is at actually—as I do this musician thing long enough, I'm learning my passion may be in the writing and recording."
All that's to say, you should catch Pickwick now—while you can. Disston is an incendiary live performer and the band have a new record full of songs they're excited about. While LoveJoys is less gritty sounding than you might be used to from the five-piece, they'll be no less emphatic on stage.
Listen to the sexy "Lying Awake In The Dark" below plus watch a few songs from their recent OPB live session. Then don't miss Pickwick on Saturday, June 24 at the Doug Fir Lounge with Cataldo. In fact, do yourself a favor and leave a comment below for your chance to win a pair of tickets.
Artist to Watch: Haley Johnsen Destroys False Idols
Brendan Swogger - May 10, 2019
It's been a journey for Haley Johnsen to find herself in the music industry, but with her debut record out May 24, she's found her direction. Win tix to her Doug Fir release show with The Weather...
How to Sell Out
Chris Young - May 1, 2019
And make a living from your music! Learn about licensing, partnership and sponsorship when our Get Paid! panel series continues at the Doug Fir on Sunday, May 19. Join Vortex, MusicPortland and...
Scenes from Day 2 of Bumbershoot featuring The Head and the Heart, Pickwick, Schoolboy Q, Schoolyard Heroes and more at the Seattle Center on August 31, 2014
Photos by Christina Bay
September 9, 2014 9:15pm
Pickwick and Lost Lander at the Red Bull Sound Select Portland showcase at the Doug Fir Lounge on Jan. 7, 2014
Photos by Josh Phillips

redpajama_set_name: RedPajamaCommonCrawl


text:
PROFIT TAX IN SERBIA IN 2018 - ALL YOU NEED TO KNOW ABOUT IT
Profit or income tax is an additional tax on earnings or some profitable income. It is delivered no later than May 15 of the current year, for the realized earnings from the previous year. This tax is not mandatory for all persons who receive income. It is mandatory only for persons whose earnings exceeds a certain non-taxable amount, and is paid over that amount.
NON-TAXABLE AMOUNT
For the year 2018, the non-taxable amount is 2,375,136 dinars and is equal to triple the amount of the average annual salary per employee, which was paid in the Republic of Serbia in 2017. For amounts exceeding the limit, income is then taxed.
By definition, non-taxable income is triple the amount of average annual earnings per employee, paid in the Republic of Serbia. According to the data of the Republic Institute for Statistics, the average annual salary per employee in the Republic of Serbia, paid in 2017, is 791,712 dinars. Based on this, the non-taxable amount for 2017 is 2,375,136 dinars.
Taxpayers qualify for the personal income tax only when they earn income threefold higher than the average monthly salary of an employee in the current year. It takes into account the citizen's salary, paid in the Republic of Serbia in the year for which the tax is determined. The main condition is that in the course of a calendar year, the income is greater than the triple amount of average annual earnings.
Who pays the income tax for citizens?
Annual tax on income of citizens is paid by the following qualified taxpayers:
Citizens who have earned income greater than the non-taxable amount,
Residents, for income realized in the Republic of Serbia and abroad,
Non-residents, for income realized in the Republic of Serbia.
Residents are persons who reside in Serbia, as well as persons who perform their business activities within the territory of the Republic of Serbia. Residents are also persons who reside in our country for 183 days or more, for a period of 12 months.
Individuals who are going to work abroad become residents, but only if they fulfill certain conditions, in accordance with the Law. Otherwise, they do not become residents. Individuals who go abroad to work in a diplomatic or consular mission are residents.
A non-resident is an individual who earns income in the Republic of Serbia, but does not fulfill the conditions for becoming a resident. He is obliged to file a tax return and pay a personal income tax.
REVENUES THAT NEEDS TO BE TAXABLE
Income that is taxable and whose total annual sum represents the total annual income are:
wages,
taxable income from independent activity (profit of entrepreneur),
base for lump-sum taxation (only according to the Tax Administration's decision),
taxable income from copyright and related rights, as well as industrial property rights,
taxable income from the issue of movables,
taxable income from issuing real estate,
taxable income of athletes and sports professionals,
all other income, from Article 85 of the Law.
Consult your authorized bookkeeper about all the details and concerns about taxable income and tax.
TAXABLE INCOME
Taxable income is the difference between the total annual collection of taxable income, deducted for taxes and contributions on the account of the income recipient, and the non-taxable amount. This means that total earnings are reduced by paid taxes and contributions, from which the non-taxable amount is deducted.
TAXATION BASE
The tax base for the personal income tax can be reduced through individual deductions. That is, in fact, the difference between taxable income and deductions. Deductions to which a taxpayer is entitled may also be personal and deductions for dependent family members. Those are:
for the taxpayer the deduction is 40%, from the average annual salary per employee,
for a dependent family member, the deduction is 15% of the average annual earnings per employee.
It is important to note that with deductions of family members there are some restrictions:
the total deduction may not exceed 50% of the taxable income,
if two or more family members are subject to annual income tax, the right to deduct can be realized only for one taxpayer.
If two or more family members are taxpayers of annual income tax, only one taxpayer, or a member of the family who is supported, can deduct a deduction on this basis. Supported family members are persons who are supported by taxpayer and they make the family community. Those are:
underage children or adopted children,
children or adopted children in full-time education or during unemployment (if they live with a taxpayer living in a household)
grandchildren (if their parents do not support them and if they live with a taxpayer in the household),
a spouse,
parents or adoptive parents.
TAXATION RATE
There are two rates of annual income tax, which are 10% and 15%. Up to the amount of 4,750,272 dinars tax is paid 10%, and over that amount 15% is paid. This means the following:
if the taxpayer realizes a taxable income of up to six average annual salaries, he will pay the tax at a rate of 10% - up to 4,750,272 dinars,
If the taxpayer has income exceeding six average annual salaries, the rate of 15% will apply. In this case, the tax is paid in such a way that up to the amount of 4,750,272 dinars (six average annual salaries), a tax rate of 10% is applied, and 15% is paid for the amount greater than this.
RESPONSIBILITIES AND PENALTIES
If the Tax Administration fails to file a tax return for income tax, penalties may be monetary or result in imprisonment. The taxpayers can be punished if they fail to submit the application and pay taxes within the legal deadline, but also if they commit other offenses:
do not submit an application,
do not submit an application at all,
if you submit an unsigned application,
if the tax return is filled in with incorrect data, and the document is not corrected before the deadline,
if they submit an application without the necessary supporting documentation and evidence, which are relevant to the determination of the tax.
DEADLINE FOR SUBMITTING TAX APPLICATION
Annual tax on citizens' income shall be reported to the competent Tax Administration, at the place of business and performance of the activity, no later than May 15 of the current year. The tax return is applied and submitted electronically or in paper form, on the prescribed tax return PPDG-2R. If submitted electronically, the taxpayer must have an electronic signature. If the tax return is completed in paper form, it must be signed. The tax return must be submitted to the Tax Administration personally, but the taxpayer may also authorize a tax proxy.


text:
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By adminOctober 6, 2013News, stainless steel hardware
A fastener is a hardware device that mechanically joins or affixes two or more objects together.
Fasteners can also be used to close a container such as a bag, a box, or an envelope; or they may involve keeping together the sides of an opening of flexible material, attaching a lid to a container, etc. There are also special-purpose closing devices, e.g. a bread clip. Fasteners used in these manners are often temporary, in that they may be fastened and unfastened repeatedly.
Some types of woodworking joints make use of separate internal reinforcements, such as dowels or biscuits, which in a sense can be considered fasteners within the scope of the joint system, although on their own they are not general purpose fasteners.
Furniture supplied in flat-pack form often uses cam dowels locked by cam locks, also known as conformat fasteners.
Items like a rope, string, wire (e.g. metal wire, possibly coated with plastic, or multiple parallel wires kept together by a plastic strip coating), cable, chain, or plastic wrap may be used to mechanically join objects; but are not generally categorized as fasteners because they have additional common uses. Likewise, hinges and springs may join objects together, but are ordinarily not considered fasteners because their primary purpose is to allow articulation rather than rigid affixment.
Other alternative methods of joining materials include: crimping, welding, soldering, brazing, taping, gluing, cementing, or the use of other adhesives. The use of force may also be used, such as withmagnets, vacuum (like suction cups), or even friction.
There are three major steel fasteners used in industries: stainless steel, carbon steel, and alloy steel. The major grade used in stainless steel fasteners: 200 series, 300 series, and 400 series.
What are the advantages of using Foreverbolt
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text:
Q: Google Sheets go to specified filter view On Open I have filter views that are named with user id's (email id).  When a user opens my sheet, I would like to run an onOpen script that opens that existing filter view.
I understand that I will need to use API, but, I have searched but cannot find anything to get started, namely how to call / open an existing filter view.
Thank you in advance!

redpajama_set_name: RedPajamaStackExchange


Customer expectation evolving faster than most of the businesses can respond. Consumers want to communicate on their terms anytime anywhere and they expect you to know that. This challenge to personalized experience to millions of diverse customers isn't achievable using a cookie cutter approach. Solutions that treating everyone with the same if then else logic cannot scale. What is needed is a dynamic technology, that can consume information, learned patterns, and adapt actions, all in real time. Five9 Genius is the solution, delivering practical AI for the contact center, taking structured data from sources including, email, chat, or web search entry, Genius predicts the reason for the customer inquiry in intelligently route and quickly resolve the issue.
Watch how a powerful single workflow engine leverages multiple data sources and drives intelligent omnichannel routing of customer interactions. Regardless of the channel, Five9 Genius can provide agent guidance on customer journey and next steps for an amazing and personalized customer experience.


text:
Nikolas Behar
Sr. Security Consultant and Adjunct Professor of Cybersecurity
Nikolas is a Sr. Security Consultant and Adjunct Professor of Cybersecurity focused on advanced adversary simulation, penetration testing, and vulnerability management. He has vast experience across many information security domains such as cyber-defense, cyber-risk, security strategy, offensive security, security awareness, and security operations.
Nikolas has worked at several organizations throughout San Diego and has been a consultant at PwC, Accenture, and Deloitte. He primarily lectures on ethical hacking, digital forensics, and information assurance. He has also sat on several information security panels, spoken at several information security conferences, and appears on local news outlets to discuss information security-related issues.
Nikolas received his M.Sc in information security from Royal Holloway, University of London and his B.A. in political science from UC, San Diego. He holds OSCP, CISSP, & CISA certifications.
How to Spot COVID-19 Themed Cybersecurity Threats
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The diversification of Sri Lankan economy and the greater representation of the diversified companies in the local stock market will help Sri Lanka to better garner more economic benefits, Thilan Wijesinghe, Chairman of National Agency for Public Private Partnership said.
Noting that Sri Lankan government doesn't have any more low hanging fruits to generate economic growth due to its inability to focus on issues relating to the micro level, especially when it comes to problem solving and execution, he said that it is important to address sources of revenue linkages, divesture of minority stakes and dead assets in certain SOEs, introduce SOEs reforms through PPPs and SOEs efficiency through process improvements to achieve set targets in the economy.
"We have a fantastic Central Bank and have a great brain trust in the Finance Ministry, but we have not been able to address issues at the micro level especially when it comes to planning, problem solving and execution." he told at the 7th edition of Capital Markets conference held in Colombo yesterday.
Noting that PPP process is not working efficiently, in Sri Lanka, he said country is using limited policy options for the fiscal consolidations. He also pointed out that implementation priorities should create a virtual circle of investor confidence, private capital inflows, SOE reforms and capital market deepening to reduce fiscal dependency on the treasury.
The PPP Agency needs to facilitate PPPs and divesture through common set of guidelines.SOE reforms and efficiency building should be multifaceted; it shouldn't not be just one formula. Divesture and privatization is only one formula. There are other models where you can take unproductive assets, just like what happened with in the case of Hambantota Port. The Hambantota Port loan was eating into all the profits that Colombo port was making. And the moment, the repayment of that loan was taken off, Sri Lanka Ports Authority balance sheet became profitable and US $ 1.2 billion was received by the government." he said.
He pointed out the need to divest non strategic assets of SOEs to strengthen the SOE balance sheet and dividends of the treasury.
Noting that most boards of loss making state enterprises comprise political appointees, Wijesinghe stressed that the Finance Ministry should look at the advisory or executive boards predominantly, manned by Finance Ministry officials as the final beneficiary of all these state owned enterprises is the Finance ministry.
Citing an example to prove this he said that the Building Materials Corporation (BMC) is not in a position to service its Rs. 600 million loan due to insufficient income. However, he said BMC has Rs. 6 - 7 billion worth of unproductive prime lands.
Furthermore, he cited sectors such as tourism, Ports, Shipping and Aviation, Knowledge based services, Financial services and Agri business as key economic drivers in the country.
Speaking on capital market, he said capital market is a curial link in mobilizing private sector financing, however he said that limited availability of long term debt, single borrowing limits, limited liquidity, under developed derivatives market, high transactions costs, and legal and regulatory impediments are some of the major impediments that hamper the growth of the market to a great extent.