Hidden symmetry in the biased Dicke model

TL;DR

This paper extends the understanding of hidden $ ext{Z}_2$ symmetry operators from the asymmetric quantum Rabi model to the N-qubit biased Dicke model, proving the existence of a $ ext{Z}_2$ symmetry at special biases.

Contribution

It generalizes the symmetry operators to the N-qubit biased Dicke model and proves they generate a $ ext{Z}_2$ symmetry for all N.

Findings

Symmetry operators for the N-qubit biased Dicke model are constructed.

These operators commute with the Hamiltonian at special biases.

The operators generate a $ ext{Z}_2$ symmetry.

Abstract

The symmetry operators generating the hidden $\mathbb{Z}_2$ symmetry of the asymmetric quantum Rabi model (AQRM) at bias $\epsilon \in \frac{1}{2}\mathbb{Z}$ have recently been constructed by V. V. Mangazeev et al. [J. Phys. A: Math. Theor. 54 12LT01 (2021)]. We start with this result to determine symmetry operators for the $N$-qubit generalisation of the AQRM, also known as the biased Dicke model, at special biases. We also prove for general $N$ that the symmetry operators, which commute with the Hamiltonian of the biased Dicke model, generate a $\mathbb{Z}_2$ symmetry.