Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport

TL;DR

This paper derives an explicit matrix product ansatz for the nonequilibrium steady state of the XXZ spin chain, revealing a pseudo-local conservation law and establishing a strict bound on ballistic spin transport at high temperature.

Contribution

It introduces a novel matrix product approach to the XXZ chain's steady state and proves a non-vanishing Mazur bound for spin Drude weight, highlighting ballistic transport regimes.

Findings

Exact pseudo-local conservation law in thermodynamic limit

Non-vanishing Mazur bound as a fractal function of anisotropy

Rigorous lower bound on high-temperature spin Drude weight

Abstract

Explicit matrix product ansatz is presented, in first two orders in the (weak) coupling parameter, for the non-equilibrium steady state of the homogeneous, nearest neighbor Heisenberg XXZ spin-1/2 chain driven by Lindblad operators which act only at the edges of the chain. The first order of the density operator becomes in thermodynamic limit an exact pseudo-local conservation law and yields -- via Mazur inequality -- a rigorous lower bound on the high temperature spin Drude weight. Such Mazur bound is a non-vanishing fractal function of the anisotropy parameter Delta for |Delta|<1.