Editing Quantum phase transition (section)

==Quantum description==

[[File:QuantumPhaseTransition.svg|thumb|Diagram of temperature (T) and pressure (p) showing the quantum critical point (QCP) and quantum phase transitions.]]

Talking about ''quantum'' phase transitions means talking about transitions at ''T'' = 0: by tuning a non-temperature parameter like pressure, chemical composition or magnetic field, one could suppress e.g. some transition temperature like the Curie or Néel temperature to 0 K.

As a system in equilibrium at zero temperature is always in its lowest-energy state (or an equally weighted superposition if the lowest-energy is degenerate), a QPT cannot be explained by [[thermal fluctuations]]. Instead, [[quantum fluctuations]], arising from [[Heisenberg's uncertainty principle]], drive the loss of [[Order and disorder (physics)|order]] characteristic of a QPT. The QPT occurs at the [[quantum critical point]] (QCP), where quantum fluctuations driving the transition diverge and become scale invariant in space and time. 

Although absolute zero is not physically realizable, characteristics of the transition can be detected in the system's low-temperature behavior near the critical point. At nonzero temperatures, classical fluctuations with an energy scale of ''k<sub>B</sub>T'' compete with the quantum fluctuations of energy scale ''ħω.'' Here ''ω'' is the characteristic frequency of the quantum oscillation and is inversely proportional to the correlation time. Quantum fluctuations dominate the system's behavior in the region where ''ħω'' > ''k<sub>B</sub>T'', known as the quantum critical region. This quantum critical behavior manifests itself in unconventional and unexpected physical behavior like novel non Fermi liquid phases. From a theoretical point of view, a phase diagram like the one shown on the right is expected: the QPT separates an ordered from a disordered phase (often, the low temperature disordered phase is referred to as 'quantum' disordered).

At high enough temperatures, the system is disordered and purely classical. Around the classical phase transition, the system is governed by classical thermal fluctuations (light blue area). This region becomes narrower with decreasing energies and converges towards the quantum critical point (QCP). Experimentally, the 'quantum critical' phase, which is still governed by quantum fluctuations, is the most interesting one.