Coherent and dissipative dynamics at quantum phase transitions
Abstract
The manybody physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the lowtemperature limit. In this review, we first give a pedagogical introduction to the equilibrium behavior of systems in that context, whose scaling framework is essentially developed by exploiting the quantumtoclassical mapping and the renormalizationgroup theory of critical phenomena at continuous phase transitions. Then we specialize to protocols entailing the outofequilibrium quantum dynamics, such as instantaneous quenches and slow passages across quantum transitions. These are mostly discussed within dynamic scaling frameworks, obtained by appropriately extending the equilibrium scaling laws. We review phenomena at firstorder quantum transitions as well, whose peculiar scaling behaviors are characterized by an extreme sensitivity to the boundary conditions, giving rise to exponentials or power laws for the same bulk system. In the last part, we cover aspects related to the effects of dissipative interactions with an environment, through suitable generalizations of the dynamic scaling at quantum transitions. The presentation is limited to issues related to, and controlled by, the quantum transition developed by closed manybody systems, treating the dissipation as a perturbation of the critical regimes, as for the temperature at the zerotemperature quantum transition. We focus on the physical conditions giving rise to a nontrivial interplay between critical modes and various dissipative mechanisms, generally realized when the involved mechanism excites only the lowenergy modes of the quantum transitions.
 Publication:

Physics Reports
 Pub Date:
 November 2021
 DOI:
 10.1016/j.physrep.2021.08.003
 arXiv:
 arXiv:2103.02626
 Bibcode:
 2021PhR...936....1R
 Keywords:

 Quantum phase transitions;
 Outofequilibrium quantum dynamics;
 Dissipative mechanisms;
 Dynamic scaling at quantum transitions;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Lattice;
 Quantum Physics
 EPrint:
 Review paper, 138 pages. Final version to appear in Physics Reports