Dissipatively dressed quasiparticles in boundary driven integrable spin chains

TL;DR

This paper introduces a framework for understanding the nonequilibrium steady states of boundary-driven integrable spin chains by using dissipatively dressed quasiparticles, providing explicit analytic expressions for their spectra.

Contribution

It develops a method to compute the spectrum of NESS in integrable spin chains via dissipation-dressed quasiparticles and derives explicit formulas for various models with boundary fields.

Findings

Dissipative dressing introduces a new singularity in the dispersion relation.

Explicit analytic expressions for dressed energies in XXX and XXZ models.

Dissipation significantly alters the NESS spectrum compared to coherent models.

Abstract

The nonequilibrium steady state (NESS) of integrable spin chains experiencing strong boundary dissipation is accounted by introducing quasiparticles with a renormalized -- dissipatively dressed -- dispersion relation. This allows us to evaluate the spectrum of the NESS in terms of the Bethe ansatz equations for a related coherent system which has the same set of eigenstates, the so-called dissipation-projected Hamiltonian. We find explicit analytic expressions for the dressed energies of the XXX and XXZ models with effective, i.e., induced by the dissipation, diagonal boundary fields, which are U(1) invariant, as well as the XXZ and XYZ models with effective non-diagonal boundary fields. In all cases, the dissipative dressing generates an extra singularity in the dispersion relation, substantially altering the NESS spectrum with respect to the spectrum of the corresponding coherent model.