You will be presented with the full text of a science research paper. Please write an abstract for this paper. Your response should include the abstract and no additional text.

Paper text:
quantum antiferromagnetism for unfrustrated systems has been one of the most extensively researched subjects in condensed matter physics .
one of the simplest models in this family , the nearest neighbor spin @xmath1 heisenberg antiferromagnet on the square lattice , has been studied extensively : analytically with spin wave  @xcite and schwinger boson approaches  @xcite and numerically with quantum monte carlo  @xcite  ( which has no `` sign problem '' for bipartite lattices ) .
that said , effects from physical imperfections such as the presence of open edges  @xcite and static non magnetic impurities  @xcite are less well understood and hence are areas of active research .    in this paper , we study quantum antiferromagnetism on the cayley tree  ( or bethe lattice  @xcite ) a bipartite lattice without loops , with the motivation of understanding the low energy spectrum of the spin half heisenberg model on this lattice .
the cayley tree has the well - known general pathology that , in the thermodynamic limit , the number of boundary sites is a finite fraction of the total number of sites ; as a consequence , different ways of approaching the thermodynamic limit may give different results in any problem based on the cayley tree .
a particular manifestation of this for the antiferromagnet is that finite trees may have a large excess of sites belonging to one sublattice over the other .
our systematic study of the low energy spectrum of the spin half heisenberg hamiltonian on the cayley tree shows that the effect of sublattice imbalance is to create a `` tower of states '' , lower than the anderson tower of states  @xcite .
a similar result was obtained by wang and sandvik  @xcite from their study of spin half antiferromagnets on diluted square lattices . aided by numerical calculations ,
we propose a framework for understanding this effect .
we also find that schwinger boson mean field theory  @xcite is a good description of the many body ground state and can reproduce many of its features quantitatively .
previous studies of this model by otsuka  @xcite and friedman  @xcite focused primarily on ground state properties and excited states were not considered in these studies .
more recently kumar et al .
@xcite have significantly extended this analysis to both the spin-1/2 and spin-1 heisenberg model .
we use all these studies as useful benchmarks for our own numerical calculations .    from a theorist s perspective
, the cayley tree achieves many simplifications which makes exact solutions possible , e.g. the bose hubbard model on this lattice was recently solved by semerijan , tarzia and zamponi  @xcite .
it is also the basis of approximations such as the brinkman - rice treatment of the hubbard model  @xcite .
more recently , it found applications in the treatment of the quantum impurity problem which is at the heart of dynamical mean field theory ( dmft )  @xcite . it does not appear that a spin model has been realized on such a topology experimentally ( though there has been interest in the study of dendrimers  @xcite ) .    in our case , the complete absence of loops makes this lattice conducive for the density matrix renormalization group ( dmrg ) algorithm  @xcite . with the dmrg method we have an explicit ( yet compact ) representation of ground and excited state many - body wavefunctions which gives us abundant information to understand the low energy properties of these systems .
in particular , reduced density matrices can be used as tools to understand properties of these states  @xcite .
the remainder of the paper is divided as follows . in section  [ sec : model ]
we introduce the model and lattices being investigated and define a measure of sublattice imbalance associated with them . in section  [ sec : dmrg ] , we give a brief overview of our implementation of the dmrg algorithm applied to generic trees . in section  [ sec : gs ] , we discuss the general properties of the ground state and excited states of the bond - centered cayley tree . in section  [ sec : sma ] , we use a variational ansatz given by the single mode approximation , in conjunction with an argument from first order perturbation theory , to explain the finite size scaling of the spin gap . finally , in section  [
sec : sbmft ] , we corroborate our observations of the ground state properties , by the use of the schwinger boson mean field theory ( sbmft ) .
we consider the nearest neighbor antiferromagnetic spin 1/2 heisenberg model with uniform coupling @xmath2 , @xmath3 in this paper , we use the spin rotational symmetry of the hamiltonian ( [ eq : heisenberg_hamiltonian ] ) , to label many body states by @xmath4 , where @xmath5 refers to the spin of the state and @xmath6 is its @xmath7 component .    on a bipartite lattice ( with sublattices _ a _ and _ b _ ) , like the cayley tree , with @xmath8 sites in sublattice _ a _ and @xmath9 sites in sublattice _
, it is rigorously known  @xcite that the ground state of the heisenberg hamiltonian has a net spin @xmath10 .
the first kind of tree we consider is the `` bond - centered '' cayley tree of the form depicted in fig .  [
fig : bond_site_center](a ) .
the number of sites @xmath11 for such a cluster is related to the `` generation '' @xmath12 by , @xmath13 since the bond centered clusters have no `` global imbalance '' i.e. @xmath14 , the ground state is a singlet ( and the monotonicity of the energy with total spin @xmath5 implies that the first excited state is a triplet ) .        as mentioned before
, the notion of `` local sublattice imbalance '' will be crucial in understanding the low energy physics . for the bond centered cluster , we define a measure of imbalance ( which we refer to as @xmath15 from here on ) by dividing the cluster at the central bond into two equal parts .
we count the excess of one sublattice over the other in one half of the cluster and multiply by 1/2 for spin 1/2 .
it can be easily shown that @xmath16 is related to the generation @xmath12 as , @xmath17 where @xmath18 is for @xmath12 odd(even ) .
[ fig : bond_site_center](b ) is the more usual way of defining a cayley tree and which we refer to as `` site - centered '' . the number of sites is related to the generation @xmath12 by , @xmath19 unlike the bond centered cluster , a global sublattice imbalance exists here which leads to a ground state spin of @xmath20 .
we measure the imbalance @xmath21 in either of the three symmetrical arms of the site centered cayley tree : specifically , we count the excess sites of one sublattice over the other ( in one arm ) and multiply by 1/2 .
this definition is particularly convenient as it gives us @xmath22 for all @xmath12 . a recent publication on the study of the heisenberg model on the cayley tree by kumar , ramasesha and soos  @xcite considers the site - centered clusters .
we confirm their results for the site - centered case , but interestingly find that the bond - centered cluster has significantly different ground and excited state properties .
we will provide some brief comparisons in section  [ sec : gs ] to illustrate this point .
how is the situation different if there is no imbalance locally ? to address this , we introduce the `` fibonacci cayley tree '' . the recipe for constructing the generation @xmath23
fibonacci - cayley tree is to combine the generation @xmath12 and @xmath24 trees by connecting their roots ( head sites ) to a common site ( which in turn serves as the root ( head site ) of the generation @xmath23 tree ) .
[ fig : bond_site_center](c ) illustrates this construction .
the total number of sites @xmath11 at generation @xmath23 is , @xmath28 observe that @xmath29 satisfies the fibonacci recursion , that is , @xmath30 , where @xmath31 is the @xmath12-th fibonacci number , which justifies the name of the tree .
the size of this lattice grows as @xmath32 where @xmath33 is the golden ratio @xmath34 . also , every 3rd generation is unbalanced by 1 and every other generation is both globally and locally balanced .
table  [ table : fibonacci ] shows the sizes of the fibonacci - cayley clusters along with the number of sites in the even and odd sublattices for up to @xmath35 generations .
.number of sites in a fibonacci - cayley tree as a function of generation @xmath12 .
@xmath36 is number of @xmath37 sublattice sites ; @xmath38 except for the entries marked with @xmath39 , in which case @xmath40 .
the total count is @xmath41 . [
cols="<,^,^,^,^,^,^,^,^,^,^,^,^ " , ]                              in the literature , the `` bethe lattice '' is often used to refer to the thermodynamic limit of the `` cayley tree '' , where the effect of boundaries is eliminated ( see for example laumann et al .
@xcite which considers random graphs of fixed connectivity ) . for the purpose of this paper
, the presence of open boundaries will play an important role in the low energy physics and so we will simply use the term `` cayley tree '' .                                                  _
templates for the solution of algebraic eigenvalue problems : a practical guide _
z.bai , j. demmel , j. dongarra , a. ruhe , and h. van der vorst society for industrial and applied mathematics , philadelphia , pa ( 2000 ) .
the expression @xmath42 is invariant under the transformation @xmath43 though it is not manifestly evident at first glance .
one can prove this , by using two results specific to a singlet state .
first , @xmath44 which equals zero for a singlet state .
second , @xmath45 which equals zero for a state with @xmath46 .
to understand the role of local sublattice imbalance in low energy spectra of @xmath0 quantum antiferromagnets , we study the @xmath0 quantum nearest neighbor heisenberg antiferromagnet on the coordination 3 cayley tree . 
 we perform many - body calculations using an implementation of the density matrix renormalization group ( dmrg ) technique for generic tree graphs . 
 we discover that the bond - centered cayley tree has a quasi - degenerate set of low lying tower of states and an `` anomalous '' singlet - triplet finite size gap scaling . for understanding the construction of the first excited state from the many - body ground state 
 , we consider a wavefunction ansatz given by the single mode approximation ( sma ) , which yields a high overlap with the dmrg wavefunction . observing the ground state entanglement spectrum leads us to a picture of the low energy degrees of freedom being `` giant spins '' arising out of sublattice imbalance , which helps us analytically understand the scaling of the finite size spin gap . 
 the schwinger boson mean field theory has been generalized to _ 
 non uniform _ lattices and ground states have been found which are spatially inhomogeneous in the mean field parameters .