Bethe-ansatz diagonalization of steady state of boundary driven integrable spin chains

Abstract: We find that the density operator of non-equilibrium steady state (NESS) of XXZ spin chain with strong ``sink and source" boundary dissipation, can be described in terms of quasiparticles, with renormalized -- dissipatively dressed -- dispersion relation. The spectrum of the NESS is then fully accounted for by Bethe ansatz equations for an associated coherent system. The dissipative dressing generates an extra singularity in the dispersion relation, which strongly modifies the NESS spectrum with respect to the spectrum of the corresponding coherent model. In particular, this leads to a dissipation-assisted entropy reduction, due to the suppression -- in the NESS spectrum -- of plain wave-type Bethe states in favor of Bethe states localized at the boundaries.