Low Temperature Physics: 42, 971 (2016); https://doi.org/10.1063/1.4969869
Физика Низких Температур: Том 42, Выпуск 11 (Ноябрь 2016), c. 1240-1267    ( к оглавлению , назад )

Dynamical quantum phase transitions

A.A. Zvyagin

Max-Planck Institut für Physik komplexer Systeme, 38 Noethnitzer Str., D-01187, Dresden, Germany

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine 47 Pr. Nauky, Kharkiv 61103, Ukraine
E-mail: Zvyagin@ilt.kharkov.ua

Received June 9, 2016


During recent years the interest to dynamics of quantum systems has grown considerably. Quantum many body systems out of equilibrium often manifest behavior, different from the one predicted by standard statistical mechanics and thermodynamics in equilibrium. Since the dynamics of a many-body quantum system typically involve many excited eigenstates, with a non-thermal distribution, the time evolution of such a system provides an unique way for investigation of non-equilibrium quantum statistical mechanics. Last decade such new subjects like quantum quenches, thermalization, pre-thermalization, equilibration, generalized Gibbs ensemble, etc. are among the most attractive topics of investigation in modern quantum physics. One of the most interesting themes in the study of dynamics of quantum many-body systems out of equilibrium is connected with the recently proposed important concept of dynamical quantum phase transitions. During the last few years a great progress has been achieved in studying of those singularities in the time dependence of characteristics of quantum mechanical systems, in particular, in understanding how the quantum critical points of equilibrium thermodynamics affect their dynamical properties. Dynamical quantum phase transitions reveal universality, scaling, connection to the topology, and many other interesting features. Here we review the recent achievements of this quickly developing part of low-temperature quantum physics. The study of dynamical quantum phase transitions is especially important in context of their connection to the problem of the modern theory of quantum information, where namely non-equilibrium dynamics of many-body quantum system plays the major role.

PACS: 05.30.Rt Quantum phase transitions;
PACS: 05.70.Ln Non-equilibrium and irreversible thermodynamics;
PACS: 03.65.Yz Decoherence; open systems; quantum statistical methods;
PACS: 64.60.Ht Dynamic critical phenomena;
PACS: 64.70.Tg Quantum phase transitions;
PACS: 75.10.Jm Quantized spin models, including quantum spin frustration.

Ключевые слова: quantum systems, dynamics, phase transitions, non-equilibrium dynamics.

Published online: September 26, 2016