From thermal to excited-state quantum phase transitions ---the Dicke model

TL;DR

This paper investigates how excited-state quantum phase transitions in the Dicke model evolve into standard thermal phase transitions when considering all angular momentum sectors, revealing they are different manifestations of the same underlying phenomenon.

Contribution

It demonstrates that excited-state and thermal phase transitions in the Dicke model are fundamentally connected, with the former transforming into the latter when all angular momentum sectors are included.

Findings

Both phase transitions share the same origin.

Logarithmic singularities are smoothed out across sectors.

Critical energy divides the spectrum into symmetry-breaking and symmetric regions.

Abstract

We study the thermodynamics of the full version of the Dicke model, including all the possible values of the total angular momentum $j$, with both microcanonical and canonical ensembles. We focus on how the excited-state quantum phase transition, which only appears in the microcanonical description of the maximum angular momentum sector, $j=N/2$, change to a standard thermal phase transition when all the sectors are taken into account. We show that both the thermal and the excited-state quantum phase transitions have the same origin; in other words, that both are two faces of the same phenomenon. Despite all the logarithmic singularities which characterize the excited-state quantum phase transition are ruled out when all the $j$-sectors are considered, the critical energy (or temperature) still divides the spectrum in two regions: one in which the parity symmetry can be broken, and another in which this symmetry is always well defined.