Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

TL;DR

This review explores the complex non-equilibrium dynamics of integrable and many-body localized quantum systems after a quench, highlighting their failure to thermalize and the emergence of novel dynamical phases.

Contribution

It provides a comprehensive overview of universal dynamics, steady states, and phase transitions in non-thermalizing quantum systems with conserved quantities.

Findings

Identification of non-thermal steady states in integrable systems

Characterization of dynamical phases beyond thermal equilibrium

Insights into phase transitions in many-body localized systems

Abstract

We review the non-equilibrium dynamics of many-body quantum systems after a quantum quench with spatial inhomogeneities, either in the Hamiltonian or in the initial state. We focus on integrable and many-body localized systems that fail to self-thermalize in isolation and for which the standard hydrodynamical picture breaks down. The emphasis is on universal dynamics, non-equilibrium steady states and new dynamical phases of matter, and on phase transitions far from thermal equilibrium. We describe how the infinite number of conservation laws of integrable and many-body localized systems lead to complex non-equilibrium states beyond the traditional dogma of statistical mechanics.