Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model

TL;DR

This paper investigates a non-Hermitian Jaynes-Cummings model, revealing exceptional points, quantum phase transitions, and phase-dependent entanglement entropy profiles.

Contribution

It uncovers the presence of exceptional points and phase transitions in the model, along with entanglement entropy analysis distinguishing different phases.

Findings

Identification of exceptional points on two-dimensional subspaces.

Observation of quantum phase transitions from real to complex eigenvalues.

Distinct entanglement entropy profiles characterize different phases.

Abstract

In this paper, we describe some interesting properties of a non-Hermitian Jaynes-Cummings model. For this particular model, it is known that the Hilbert space can be described by infinitely-many two-dimensional invariant (closed) subspaces, together with the global ground state. We expose the appearance of exceptional points on such two-dimensional subspaces, together with quantum phase transitions marking the transition from real to complex eigenvalues. We also compute the spin-oscillator entanglement entropy on each invariant subspace to show that the two phases can be distinguished by their distinct entanglement-entropy profiles.