Hidden $sl(2)$-algebraic structure in Rabi model and its 2-photon and two-mode generalizations

TL;DR

This paper reveals a hidden $sl(2)$-algebraic structure in the quantum Rabi model and its generalizations, explaining their quasi-exact solvability and marking the first such discovery in spin-boson systems lacking $U(1)$ symmetry.

Contribution

It uncovers a hidden $sl(2)$ algebraic structure in the Rabi model and its variants, providing new insights into their solvability and symmetry properties.

Findings

Identification of hidden $sl(2)$ structure in Rabi models

Explanation of quasi-exact solvability through algebraic structure

First discovery of such structure in systems without $U(1)$ symmetry

Abstract

It is shown that the (driven) quantum Rabi model and its 2-photon and 2-mode generalizations possess a hidden $sl(2)$-algebraic structure which explains the origin of the quasi-exact solvability of these models. It manifests the first appearance of a hidden algebraic structure in quantum spin-boson systems without $U(1)$ symmetry.