Path integral approach to the full Dicke model with dipole-dipole interaction

TL;DR

This paper develops a path integral method to analyze the full Dicke model with dipole-dipole interactions, determining phase transition conditions at finite and zero temperature.

Contribution

It introduces a comprehensive path integral approach to the full Dicke model including dipole-dipole interactions, deriving critical temperatures and couplings.

Findings

Calculated free energy in the thermodynamic limit.

Determined critical temperature for superradiant phase transition.

Recovered known quantum critical coupling at zero temperature.

Abstract

We consider the full Dicke spin-boson model composed by a single bosonic mode and an ensemble of $N$ identical two-level atoms with different couplings for the resonant and anti-resonant interaction terms, and incorporate a dipole-dipole interaction between the atoms. Assuming that the system is in thermal equilibrium with a reservoir at temperature $\beta^{-1}$, we compute the free energy in the thermodynamic limit $N\rightarrow\infty$ in the saddle-point approximation to the path integral and determine the critical temperature for the superradiant phase transition. In the zero temperature limit, we recover the critical coupling of the quantum phase transition, presented in the literature.