Quantum critical point
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A quantum critical point is a point in the phase diagram of a material where a continuous phase transition takes place at absolute zero. A quantum critical point is typically achieved by a continuous suppression of a nonzero temperature phase transition to zero temperature by the application of a pressure, field, or through doping. Conventional phase transitions occur at nonzero temperature when the growth of random thermal fluctuations leads to a change in the physical state of a system. Condensed matter physics research over the past few decades has revealed a new class of phase transitions called quantum phase transitions[1] which take place at absolute zero. In the absence of the thermal fluctuations which trigger conventional phase transitions, quantum phase transitions are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle.
Overview
Within the class of
At a quantum critical point, the critical fluctuations are quantum mechanical in nature, exhibiting scale invariance in both space and in time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of a quantum critical point is felt over a wide range of temperatures above the quantum critical point, so the effect of quantum criticality is felt without ever reaching absolute zero. Quantum criticality was first observed in ferroelectrics, in which the ferroelectric transition temperature is suppressed to zero.
A wide variety of metallic
Quantum critical endpoints
Quantum critical points arise when a susceptibility diverges at zero temperature. There are a number of materials (such as CeNi2Ge2[3]) where this occurs serendipitously. More frequently a material has to be tuned to a quantum critical point. Most commonly this is done by taking a system with a second-order phase transition which occurs at nonzero temperature and tuning it—for example by applying pressure or magnetic field or changing its chemical composition. CePd2Si2 is such an example,[4] where the antiferromagnetic transition which occurs at about 10K under ambient pressure can be tuned to zero temperature by applying a pressure of 28,000 atmospheres.[5] Less commonly a first-order transition can be made quantum critical. First-order transitions do not normally show critical fluctuations as the material moves discontinuously from one phase into another. However, if the first order phase transition does not involve a change of symmetry then the phase diagram can contain a critical endpoint where the first-order phase transition terminates. Such an endpoint has a divergent susceptibility. The transition between the liquid and gas phases is an example of a first-order transition without a change of symmetry and the critical endpoint is characterized by critical fluctuations known as critical opalescence.
A quantum critical endpoint arises when a nonzero temperature critical point is tuned to zero temperature. One of the best studied examples occurs in the layered ruthenate metal, Sr3Ru2O7 in a magnetic field.[6] This material shows metamagnetism with a low-temperature first-order metamagnetic transition where the magnetization jumps when a magnetic field is applied within the directions of the layers. The first-order jump terminates in a critical endpoint at about 1 kelvin. By switching the direction of the magnetic field so that it points almost perpendicular to the layers, the critical endpoint is tuned to zero temperature at a field of about 8 teslas. The resulting quantum critical fluctuations dominate the physical properties of this material at nonzero temperatures and away from the critical field. The resistivity shows a non-Fermi liquid response, the effective mass of the electron grows and the magnetothermal expansion of the material is modified all in response to the quantum critical fluctuations.
Notes
References
- Cyril Domb (1996). The critical point: a historical introduction to the modern theory of critical phenomena. Taylor and Francis. ISBN 9780748404353.
- Hertz, J. (1976). "Quantum Critical Phenomena". Phys. Rev. B. 14 (3): 1165–1184. .
- M.A. Continentino (2001). Quantum Scaling in Many-Body Systems. World Scientific.
- P. Coleman; A. J. Schofield (2005). "Quantum criticality". Nature. 433 (7023): 226–229. S2CID 4394166.
- E.G. Dalla Torre; et al. (2010). "Quantum critical states and phase transitions in the presence of non-equilibrium noise". Nature Physics. 6 (10): 806–810. S2CID 27610619.
- Carr, Lincoln D. (2010). Understanding Quantum Phase Transitions. CRC Press. ISBN 978-1-4398-0251-9.
- Mariano de Souza (2020). "Unveiling the Physics of the Mutual Interactions in Paramagnets". Scientific Reports. Vol. 10. .