The Dicke model as the contraction limit of a pseudo-deformed Richardson-Gaudin model

TL;DR

This paper demonstrates how the Dicke model can be derived as a contraction limit of a pseudo-deformed Richardson-Gaudin model, establishing its integrability and connecting it to su(2)-based models.

Contribution

It introduces a novel approach to derive the Dicke model from a pseudo-deformed Richardson-Gaudin model and proves its integrability through conserved charges and Bethe Ansatz solutions.

Findings

Dicke model obtained as contraction limit of pseudo-deformed Richardson-Gaudin model

Integrability of the Dicke model established via conserved charges and Bethe Ansatz

Connection between su(2)-based Richardson-Gaudin models and the Dicke model shown

Abstract

The Dicke model is derived in the contraction limit of a pseudo-deformation of the quasispin algebra in the su(2)-based Richardson-Gaudin models. Likewise, the integrability of the Dicke model is established by constructing the full set of conserved charges, the form of the Bethe Ansatz state, and the associated Richardson-Gaudin equations. Thanks to the formulation in terms of the pseudo-deformation, the connection from the su(2)-based Richardson-Gaudin model towards the Dicke model can be performed adiabatically.