Coherent and dissipative dynamics at quantum phase transitions

TL;DR

This review explores the equilibrium and out-of-equilibrium dynamics of quantum phase transitions, including dissipative effects, emphasizing scaling laws, boundary sensitivities, and low-energy mode interactions.

Contribution

It provides a comprehensive analysis of quantum critical dynamics, extending equilibrium scaling frameworks to out-of-equilibrium and dissipative regimes in many-body systems.

Findings

Dynamic scaling laws are extended to out-of-equilibrium protocols.

First-order quantum transitions exhibit boundary-sensitive scaling behaviors.

Dissipative interactions can be incorporated as perturbations affecting critical modes.

Abstract

The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature 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 quantum-to-classical mapping and the renormalization-group theory of critical phenomena at continuous phase transitions. Then we specialize to protocols entailing the out-of-equilibrium 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 first-order 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 many-body systems, treating the dissipation as a perturbation of the critical regimes, as for the temperature at the zero-temperature 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 low-energy modes of the quantum transitions.