Excited-state quantum phase transitions

TL;DR

This paper reviews excited-state quantum phase transitions (ESQPTs) in many-body systems, discussing their signatures, effects on thermodynamics and dynamics, and potential generalizations in various quantum systems.

Contribution

It provides a comprehensive classification of ESQPT signatures and explores their implications across different physical phenomena and system types.

Findings

Identification of typical ESQPT signatures in spectra

Analysis of thermodynamic consequences of ESQPTs

Discussion of dynamic effects and generalizations

Abstract

We review the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. We classify typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics and outline a variety of quantum systems in which they occur. We describe thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving. We hint at some generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems.