Critical Spectrum and Quantum Criticality in the Two-Photon Rabi-Stark Model

TL;DR

This paper analyzes the spectral properties and quantum criticality of the two-photon Rabi-Stark model, revealing conditions for spectral collapse and a unique quantum phase transition with implications for quantum systems.

Contribution

It provides an exact solution for the model, deriving a spectral collapse condition and identifying a new universality class for the quantum phase transition.

Findings

Complete spectral collapse occurs at a critical coupling.

Energy gap closes at the transition point, indicating a quantum phase transition.

Bound states approach the threshold exponentially in spectral collapse.

Abstract

We investigate the spectral properties and quantum criticality of the two-photon Rabi-Stark model. Using the exact solution of this model, we rigorously derive a condition for complete spectral collapse, where all bound states vanish. In this case, the energy gap closes at a critical coupling, signaling a continuous quantum phase transition. The corresponding gap exponent differs from those in both the one-photon Rabi-Stark model and the quantum Rabi model, suggesting a distinct universality class. While in the general case, an infinite number of discrete bound states exist when spectral collapse occur and the energy gap remains open. By mapping to an inverse square potential well, these bound levels approach the threshold energy exponentially. Our results offer new insights into novel spectral phenomena in nonlinear quantum Rabi models, with potential implications for experimental realizations in circuit QED and trapped ion systems.