Phase transitions of the Dicke model: a unified perspective

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.

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• Mixed eigenstates in the Dicke model: Statistics and power-law decay of the relative proportion in the semiclassical limit
• Phase Transitions in the Anisotropic Dicke-Stark Model with $A$-square terms
• Quantum multifractality as a probe of phase space in the Dicke model
• Comment on 'Revisiting the phase transitions of the Dicke model'
• Transition to chaos in extended systems and their quantum impurity models