Dynamical quantum phase transitions: a review

TL;DR

This review discusses the concept of dynamical quantum phase transitions, exploring their theoretical foundations, experimental observations, and future research directions in nonequilibrium quantum many-body systems.

Contribution

It provides a comprehensive pedagogical overview of dynamical quantum phase transitions, highlighting recent theoretical and experimental progress in nonequilibrium quantum dynamics.

Findings

Identification of phase transitions in time with nonanalytic behavior at critical times

Summary of experimental observations of dynamical quantum phase transitions

Discussion of open questions and future research directions

Abstract

Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium paradigm. While these states promise to show properties not constrained by equilibrium principles such as the equal a priori probability of the microcanonical ensemble, identifying general properties of nonequilibrium quantum dynamics remains a major challenge especially in view of the lack of conventional concepts such as free energies. The theory of dynamical quantum phase transitions attempts to identify such general principles by lifting the concept of phase transitions to coherent quantum real-time evolution. This review provides a pedagogical introduction to this field. Starting from the general setting of nonequilibrium dynamics in closed quantum many-body systems, we give the definition of dynamical quantum phase transitions as phase transitions in time with physical quantities becoming nonanalytic at critical times. We summarize the achieved theoretical advances as well as the first experimental observations, and furthermore provide an outlook onto major open questions as well as future directions of research.