Phase transitions of the Dicke model: a unified perspective

TL;DR

This paper provides a comprehensive analysis of the Dicke model's phase transitions, revealing multifractality, exact thermal transition temperature, and a new upper cut-off energy, unifying different transition types with various eigenvector properties.

Contribution

It offers a unified perspective on the Dicke model's phase transitions, including quantum, thermal, and excited state transitions, with new analytical and numerical insights.

Findings

Ground state in super-radiant phase exhibits multifractality.

Exact analytical expression for thermal transition temperature.

Discovery of a new upper cut-off energy in excited state transitions.

Abstract

The Dicke model exhibits a variety of phase transitions. The quantum phase transition from the normal phase to the super-radiant phase is marked by a dramatic change in the scaling of the participation ratio. We find that the ground state in the super-radiant phase exhibits multifractality manifest in the participation ratio scaling as the square root of the full Hilbert space dimension. The thermal phase transition temperature, for which we obtain an exact analytical expression, is strikingly captured by the mutual information between two spins. In the excited state quantum phase transition within the super-radiant phase, we discover a new upper cut-off energy; the central energy band between the lower and upper cut-off energies shows distinctly different behaviour. This finding is corroborated with the aid of several eigenvector properties: von Neumann entanglement entropy between spins and bosons, the mean photon number, concurrence between two spins, and participation ratio. Thus we obtain a unified picture for the three different kinds of phase transitions.