Dissipative dynamics in open XXZ Richardson-Gaudin models

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