Integrable spin-boson interaction in the Tavis-Cummings model from a generic boundary twist

TL;DR

This paper develops an exact solution for a spin-boson interaction model within the Tavis-Cummings framework, employing quantum inverse scattering and boundary twists, revealing integrability in a generalized boundary condition setting.

Contribution

It introduces a novel integrable spin-boson model with generic boundary twists and solves it exactly using a mapping to an auxiliary spin system and Baxter's Q-matrix method.

Findings

Exact solution for the spin-boson model with twisted boundary conditions

Mapping of the transfer matrix to an auxiliary spin system

Application of Baxter's Q-matrix method to diagonalize the transfer matrix

Abstract

We construct models describing interaction between a spin $s$ and a single bosonic mode using a quantum inverse scattering procedure. The boundary conditions are generically twisted by generic matrices with both diagonal and off-diagonal entries. The exact solution is obtained by mapping the transfer matrix of the spin-boson system to an auxiliary problem of a spin-$j$ coupled to the spin-$s$ with general twist of the boundary condition. The corresponding auxiliary transfer matrix is diagonalized by a variation of the method of $Q$-matrices of Baxter. The exact solution of our problem is obtained applying certain large-$j$ limit to $su(2)_j$, transforming it into the bosonic algebra.