Dissipative dynamics in open XXZ Richardson-Gaudin models

TL;DR

This paper analyzes the dissipative dynamics of open XXZ Richardson-Gaudin models, revealing phase transitions and spectral properties through an exact Bethe ansatz solution, highlighting the interplay of non-Hermitian physics and quantum dissipation.

Contribution

It provides the first exact Bethe ansatz solution for an open XXZ Richardson-Gaudin model with detailed spectral analysis and phase transition characterization.

Findings

Spectrum transitions from complex to real eigenvalues at exceptional points.

Steady state exhibits logarithmic decay rate growth with system size.

Large coupling strengths lead to quantized ratios of imaginary to real eigenvalues.

Abstract

In specific open systems with collective dissipation the Liouvillian can be mapped to a non-Hermitian Hamiltonian. We here consider such a system where the Liouvillian is mapped to an XXZ Richardson-Gaudin integrable model and detail its exact Bethe ansatz solution. While no longer Hermitian, the Hamiltonian is pseudo-Hermitian/PT-symmetric, and as the strength of the coupling to the environment is increased the spectrum in a fixed symmetry sector changes from a broken pseudo-Hermitian phase with complex conjugate eigenvalues to a pseudo-Hermitian phase with real eigenvalues, passing through a series of exceptional points and associated dissipative quantum phase transitions. The homogeneous limit supports a nontrivial steady state, and away from this limit this state gives rise to a slow logarithmic growth of the decay rate (spectral gap) with system size. Using the exact solution, it is furthermore shown how at large coupling strengths the ratio of the imaginary to the real part of the eigenvalues becomes approximately quantized in the remaining symmetry sectors.