Excited-State Quantum Phase Transitions in Dicke Superradiance Models

TL;DR

This paper analytically investigates excited-state quantum phase transitions in Dicke superradiance models, revealing how critical behavior depends on energy and model parameters, with results analogous to known models like Lipkin-Meshkov-Glick.

Contribution

It provides the first analytical derivation of quantities related to excited-state quantum phase transitions in Dicke models, highlighting the dependence on energy and interaction parameters.

Findings

Singular behavior in the density of states derivative

Observable quantities show non-analyticities at critical energies

Criticality varies with energy and model parameters

Abstract

We derive analytical results for various quantities related to the excited-state quantum phase transitions in a class of Dicke superradiance models in the semiclassical limit. Based on a calculation of a partition sum restricted to Dicke states, we discuss the singular behavior of the derivative of the density of states and find observables like the mean (atomic) inversion and the boson (photon) number and its fluctuations at arbitrary energies. Criticality depends on energy and a parameter that quantifies the relative weight of rotating versus counter-rotating terms, and we find a close analogy to the logarithmic and jump-type non-analyticities known from the Lipkin-Meshkov-Glick model.