Exact solution for the inhomogeneous Dicke model in the canonical ensemble: thermodynamical limit and finite-size corrections

TL;DR

This paper provides an exact solution for the inhomogeneous Dicke model in the thermodynamic limit and finite-size corrections, extending existing methods to analyze disordered two-level systems interacting with a boson field.

Contribution

It extends the Richardson-Gaudin equations approach to the Dicke model, enabling calculation of energies and finite-size effects for arbitrary spin energy distributions.

Findings

Derived expressions for ground and excited state energies.

Analyzed finite-size corrections and spectral gap evolution.

Identified phase diagram regions with significant finite-size effects.

Abstract

We consider an exactly solvable inhomogeneous Dicke model which describes an interaction between a disordered ensemble of two-level systems with single mode boson field. The existing method for evaluation of Richardson-Gaudin equations in the thermodynamical limit is extended to the case of Bethe equations in Dicke model. Using this extension, we present expressions both for the ground state and lowest excited states energies as well as leading-order finite-size corrections to these quantities for an arbitrary distribution of individual spin energies. We then evaluate these quantities for an equally-spaced distribution (constant density of states). In particular, we study evolution of the spectral gap and other related quantities. We also reveal regions on the phase diagram, where finite-size corrections are of particular importance.