Quantum critical points arise when a material is dominated by thermal and quantum fluctuations. The result is a very unusual state of matter where, in a metal, the electrons are rapidly scattered and can adopt other forms of order like superconductivity, novel types of magnetism, or even more mysteriously, unidentified "dark order".
Put more rigorously, the material must be tuned to a point where, at zero temperature, it would have a diverging susceptibility. This can occur when a continuous phase transition is suppressed to zero temperature, perhaps by applying pressure, making a quantum phase transition. Alternatively the critical end-point of a first order transition can be adjusted to occur at zero temperature as was done by our experimental collaborators on the material Sr2Ru3O7 shown here.
Although you can never reach the absolute zero of temperature, the presence of a quantum critical point influences a wide region of the phase diagram. This is often shown by the resistivity of the metal having a temperature dependence that is closer to T than the T2 expected in a correlated metal. The figure shows the powerlaw in the resistivity at a quantum critical end-point.
The underlying theory behind quantum critical points combines the theory of quantum mechanics with the theory of phase transitions. Both theories are well tested separately. One of the significant challenges to the field is that combining these theories often does not lead to a theory that is consistent with experiments. We are actively researching this.
Finally, proximity to a quantum critical point may be the cause of unusual properties in a variety of materials even when the quantum critical point itself has not been observed. In such materials the quantum critical point might only be observable with an unphysical tuning parameter like negative-pressure. Yet the proximity to quantum criticality would still leave a shadow on the phase diagram of the material.
For some general information on quantum criticality, see
Nature 433, 226 (2005)
Science 294, 329-332 (2001)
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