Dissipative dynamics in open XXZ Richardson-Gaudin models

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.

7+4 pages

References in corpus (12)

• The physics of exceptional points
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• From Interacting Particles to Equilibrium Statistical Ensembles
• Gaudin models solver based on the Bethe ansatz/ordinary differential equations correspondence
• Constructing Integrable Lindblad Superoperators
• PT-symmetric quantum Liouvillian dynamics
• An eigenvalue-based method and determinant representations for general integrable XXZ Richardson-Gaudin models
• Dynamical signatures of topological order in the driven-dissipative Kitaev chain
• Linked cluster expansions for open quantum systems on a lattice
• Richardson-Gaudin integrability in the contraction limit of the quasispin
• Inner products in integrable Richardson-Gaudin models

Cited by in corpus (4)

• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Many-Body Open Quantum Systems
• Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
• Exceptional Spectral Phase in a Dissipative Collective Spin Model