Quantum phase transition

In physics, a quantum phase transition ( QPT or English quantum phase transition, ) is a phase transition between different quantum phases, which are different " states of matter " (analogous to "liquid", "solid"; magnetic, non-magnetic, etc. ) at absolute zero temperature, T = 0 K, where no thermal fluctuations occur, but only so-called quantum fluctuations. In contrast to the "classical" ( thermischen! ) phase transitions can quantum phase transitions thus occur only if at absolute zero temperature, a non-temperature -like physical parameters such as the pressure or a magnetic field is varied. The phase transition is due to an abrupt qualitative material change of the ground state of this many-body system by the quantum fluctuations.

Classification

A distinction phase transitions " first" and " second order ", depending on whether one of the first derivatives, or only one of the second derivatives of the thermodynamic potential is zero (usually the former is the case, the so-called critical point is, however, to phase transitions second order ). Also quantum phase transitions may be phase transitions of second order. They are similar to the transition from non-magnetic to the magnetic phase of a ferromagnetic system drops below the so-called Curie temperature. ( Here, however, one is always at T = 0 )

It is otherwise appropriate, quantum phase transitions and classical phase transitions (also called " thermal phase transitions " called ) to face. A " classical phase transition " describes a sharp qualitative material change in the thermal system properties. It signals a reorganization of the particles ( or their characteristics ). A typical example of a classic phase transition is the freezing, the ( not only in water!) The transition from the liquid to the solid state describes. Classical phase transitions are based on the conflict between the energy of the system and the entropy of its thermal fluctuations. In a classical system, the entropy vanishes at absolute zero; why can not a classical phase transition at T = 0 occur.

Continuous transitions (including the " second order "! ) Lead an "ordered phase " into a " disordered " about, the ordered state is quantitatively described by a so-called order parameter ( it is zero in the disordered phase and rises when falling below the transition parameter continuous on positive values ​​). For the above mentioned ferromagnetic phase transition of the order parameter of the internal magnetization of the system would meet. But although the order parameter itself is ( a thermal average! ) In the disordered phase is zero, this is not true for its fluctuations. They will get close to the so-called critical point even infinite range. And hangs the range with the so-called " correlation length " together, and typical fluctuations decay with a characteristic " correlation time ", provided with so-called " critical exponent " z and the following:

Here ε is the relative deviation of the temperature from the critical value.

The Critical behavior of thermal phase transitions is fully described by classical physics, even if it is for example in superconductivity to a so-called macroscopic quantum phenomenon. In the quantum phase transitions is, however, to phenomena at T = 0

When we speak of quantum phase transitions, one thus always means phase transition at T = 0 By changing a direction different from the temperature parameter such as pressure, chemical composition, or the magnetic field could be a transition temperature such as a Curie or Neel temperature, lowered to 0 K. But since this, as I said, can not produce a quantum phase transition, one has to fall back again on quantum fluctuations. The terminology used is still the same as in the classical case.

At finite temperature, the quantum fluctuations and thermal fluctuations are competing with each other. The respective energy scales are respectively. For quantum fluctuations dominate the system's behavior, but for the "scaling " along an axis passing through the critical point QCP the respective vertical distance of said axis is relevant; the scaling behavior is first violated when, for example, is comparable. This results in a pointed, increasingly wider scale quantum critical region around the y- axis by QCP. ( The amount of can be regarded as the characteristic frequency of a quantum oscillation and is inversely proportional to the correlation time. ) Consequently, it should be possible to also see traces of a quantum transition at finite temperatures. These traces may show up in an unconventional physical behavior, for example in quantum liquids which differ from the usual Fermi behavior.

So you can expect a phase diagram as shown in the adjacent sketch. The boundary lines outside the ordered state for T > 0 only blurred defined as so-called "crossover lines". The visibility region of the quantum behavior is quite large in any case.

Systems

Features that lead to quantum phase transitions likely to occur in one-dimensional systems, since they allow for many pictures. Accordingly, such systems, such as spin chains and ladders, but also the so-called spin ice are examined primarily.