# Construction of the steady state density matrix and quasilocal charges for the spin-1/2 XXZ chain with boundary magnetic fields

## TL;DR

This paper constructs the nonequilibrium steady state density matrix for the spin-1/2 XXZ chain with boundary magnetic fields, expressing it via a non-Hermitian transfer operator that reveals quasilocal charges, and discusses optimizing the Mazur bound for high-temperature transport.

## Contribution

It introduces a method to explicitly construct the NESS density operator for the XXZ chain with boundary fields using Lax operators and relates it to quasilocal charges, advancing understanding of boundary-driven quantum systems.

## Key findings

- Explicit NESS density operator in terms of Lax operators.
- Identification of a non-Hermitian transfer operator forming quasilocal charges.
- Discussion on optimizing the Mazur bound for high-temperature Drude weight.

## Abstract

We construct the nonequilibrium steady state (NESS) density operator of the spin-1/2 XXZ chain with non-diagonal boundary magnetic fields coupled to boundary dissipators. The Markovian boundary dis- sipation is found with which the NESS density operator is expressed in terms of the product of the Lax operators by relating the dissipation parameters to the boundary parameters of the spin chain. The NESS density operator can be expressed in terms of a non-Hermitian transfer operator (NHTO) which forms a commuting family of quasilocal charges. The optimization of the Mazur bound for the high temperature Drude weight is discussed by using the quasilocal charges and the conventional local charges constructed through the Bethe ansatz.