New symmetry in the Rabi model

TL;DR

This paper explores a previously unrecognized symmetry in the Rabi model, detailing the conditions for its existence, form, and explicit construction, expanding understanding of the model's underlying structure.

Contribution

It introduces a new symmetry in the Rabi model, providing explicit conditions and construction methods for this observable, which was previously unrecognized.

Findings

Identification of a new nonlocal $Z_2$ symmetry in the Rabi model

Explicit construction of the symmetry observable

Enhanced understanding of the model's symmetry structure

Abstract

It is recognised that, apart from the total energy conservation, there is a nonlocal $\mathbb{Z}_2$ and a somewhat hidden symmetry in this model. Conditions for the existence of this observable, its form, and its explicit construction are presented.