Excited-state quantum phase transitions

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.

Automated summary

The paper reviews the effects of excited-state quantum phase transitions (ESQPTs) in interacting many-body systems with finite numbers of collective degrees of freedom. It classifies typical ESQPT signatures in the spectra of energy eigenstates with respect to the underlying classical dynamics, outlining a variety of quantum systems in which they occur. The thermodynamic and dynamic consequences of ESQPTs, like those in microcanonical thermodynamics, quantum quench dynamics, and in the response to nearly adiabatic or periodic driving are described. Suggestions for generalizations of the ESQPT concept in periodic lattices and in resonant tunneling systems are also mentioned.