Exact solutions for a family of spin-boson systems

TL;DR

This paper derives exact solutions for a family of spin-boson systems using polynomial Lie algebra representations, unifying several well-known physical models under a common mathematical framework.

Contribution

It introduces a novel algebraic approach to solve a broad class of spin-boson models exactly, encompassing multiple important physical systems.

Findings

Exact solutions for a family of spin-boson Hamiltonians

Unification of models like Bose-Hubbard, Lipkin-Meshkov-Glick, and Tavis-Cummings

Application of polynomial Lie algebra representations

Abstract

We obtain the exact solutions for a family of spin-boson systems. This is achieved through application of the representation theory for polynomial deformations of the $su(2)$ Lie algebra. We demonstrate that the family of Hamiltonians includes, as special cases, known physical models which are the two-site Bose-Hubbard model, the Lipkin-Meshkov-Glick model, the molecular asymmetric rigid rotor, the Tavis-Cummings model, and a two-mode generalisation of the Tavis-Cummings model.