Quantum Critical Point

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A Quantum critical point is a special class of continuous phase transition that takes place at the absolute zero of temperature, typically in a material where the phase transition temperature has been driven to zero by the application of a pressure, field or through doping. Conventional phase transitions occur at finite 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 a quantum phase transition, which take place at absolute zero, and which are driven by the zero point quantum fluctuations associated with Heisenberg's uncertainty principle.

Within the class of phase transitions, there are two main categories - at a first order phase transition, the properties change discontinuously, as in the melting of solid, whereas at a second order phase transition, the state of the system changes in a continuous fashion. Second-order phase transitions are marked by the growth of fluctuations on ever longer length-scales. These fluctuations are called "critical fluctuations". At the critical point where a second-order transition occurs the critical fluctuations are scale invariant and extend over the entire system. At a finite temperature phase transition, the fluctuations that develop at a critical point are governed by classical physics, because their characteristic energy is always smaller than the characteristic Boltzmann thermal energy k_BT.

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 ferromagnets and antiferromagnets have been observed to develop quantum critical behavior when their magnetic transition temperature is driven to zero through the application of pressure, chemical doping or magnetic fields. In these cases, the properties of the metal are radically transformed by the critical fluctuations, departing qualitatively from the standard Fermi liquid behavior, to form a metallic state sometimes called a "non Fermi liquid" or a "strange metal". There is particular interest in these unusual metallic states, which are believed to exhibit a marked preponderence towards the development of superconductivity.

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