# Solution of the Lindblad equation for spin helix states

## TL;DR

This paper presents an exact solution to the Lindblad equation for quantum spin systems with boundary-driven dissipation, revealing pure states with helical magnetization and superdiffusive spin currents in various dimensions.

## Contribution

It introduces a method to solve the many-body Lindblad equation exactly for boundary-driven spin systems in any dimension, including non-integrable models, with explicit solutions for the stationary states.

## Key findings

- Exact pure stationary states with helical magnetization profiles
- Superdiffusive ballistic spin currents independent of system size
- Applicability to higher-dimensional and non-integrable spin models

## Abstract

Using Lindblad dynamics we study quantum spin systems with dissipative boundary dynamics that generate a stationary nonequilibrium state with a non-vanishing spin current that is locally conserved except at the boundaries. We demonstrate that with suitably chosen boundary target states one can solve the many-body Lindblad equation exactly in any dimension. As solution we obtain pure states at any finite value of the dissipation strength and any system size. They are characterized by a helical stationary magnetization profile and a superdiffusive ballistic current of order one, independent of system size even when the quantum spin system is not integrable. These results are derived in explicit form for the one-dimensional spin-1/2 Heisenberg chain and its higher-spin generalizations (which include for spin-1 the integrable Zamolodchikov-Fateev model and the bi-quadratic Heisenberg chain). The extension of the results to higher dimensions is straightforward.