Asymptotic behavior of observables in the asymmetric quantum Rabi model

TL;DR

This paper investigates the asymptotic behavior of observables in the asymmetric quantum Rabi model, revealing spectral degeneracies linked to hidden symmetries and analyzing eigenstate expectations in different coupling regimes.

Contribution

It introduces a detailed analysis of the asymptotic properties of observables and constructs a parent Hamiltonian reflecting the model's symmetries in the integer case.

Findings

Spectral degeneracies occur at integer asymmetry parameters.

Distinct asymptotic behaviors are observed between integer and noninteger cases.

A parent Hamiltonian with matching symmetries is constructed.

Abstract

The asymmetric quantum Rabi model with broken parity invariance shows spectral degeneracies in the integer case, that is when the asymmetry parameter equals an integer multiple of half the oscillator frequency, thus hinting at a hidden symmetry and accompanying integrability of the model. We study the expectation values of spin observables for each eigenstate and observe characteristic differences between the integer and noninteger cases for the asymptotics in the deep strong coupling regime, which can be understood from a perturbative expansion in the qubit splitting. We also construct a parent Hamiltonian whose exact eigenstates possess the same symmetries as the perturbative eigenstates of the asymmetric quantum Rabi model in the integer case.