A note on symmetry reductions of the Lindblad equation: transport in constrained open spin chains

TL;DR

This paper investigates how symmetry reductions in the Lindblad equation influence quantum transport in constrained open spin chains, revealing multiple steady states and sub-diffusive behavior in large systems.

Contribution

It identifies a unique discrete symmetry in the Liouvillean framework that simplifies dynamics and explains the emergence of multiple steady states in open quantum spin chains.

Findings

Multiple steady states exist due to symmetry

Sub-diffusive spin transport observed in large systems

Symmetry reduces the effective dynamics of the system

Abstract

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global `microcanonical' constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry which is particular to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than what would be expected in the standard Hilbert space formalism and establishes existence of multiple steady states. Interestingly, numerical simulations of the XXZ model suggest that a pair of distinct non-equilibrium steady states becomes indistinguishable in the thermodynamic limit, and exhibit sub-diffusive spin transport in the easy-axis regime of anisotropy Delta > 1.