Addendum to `Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model'

TL;DR

This paper clarifies the distinction between different types of exceptional points in the eigenspectrum of the generalized Rabi model, expanding on previous algebraic solutions and addressing previously overlooked exceptional points.

Contribution

It provides a detailed discussion distinguishing between subsets of exceptional points in the eigenspectrum, extending prior algebraic analysis.

Findings

Clarification of the distinction between exceptional parts of the eigenspectrum

Discussion of subset of exceptional points not previously determined

Extension of algebraic solutions to include additional exceptional points

Abstract

In our recent paper (Li and Batchelor J. Phys. A: Math. Theor. 48, 454005 (2015)) we obtained exceptional points in the eigenspectrum of the generalized Rabi model in terms of a set of algebraic equations. We also gave a proof for the number of roots of the constraint polynomials defining these exceptional solutions as a function of the system parameters and discussed the number of crossing points in the eigenspectrum. This approach however, only covered a subset of all exceptional points in the eigenspectrum. In this addendum, we clarify the distinction between the exceptional parts of the eigenspectrum for this model and discuss the subset of exceptional points not determined in our paper.