Integrable non-equilibrium steady state density operators for boundary driven XXZ spin chains: observables and full counting statistics

TL;DR

This paper reviews exact solutions for the non-equilibrium steady states of boundary-driven XXZ spin chains, focusing on observables and full counting statistics within the Lindblad framework, highlighting recent advances in integrable quantum systems.

Contribution

It summarizes known exact solutions for steady states of boundary-driven XXZ spin chains and details methods to compute observables and current statistics.

Findings

Exact solutions for steady states of XXZ chains are reviewed.

Methods for calculating physical observables are discussed.

Full counting statistics of spin current are analyzed.

Abstract

We will review some known exact solutions for the steady state of the open quantum Heisenberg $XXZ$ spin chain coupled to a pair of baths [Phys. Rev. Lett. 107, 137201 (2011).]. The dynamics is modelled by the Lindblad master equation. We also review how to calculate some relevant physical observables and provide the statistics of spin current assuming the spin chain is weakly coupled to the baths [Phys. Rev. Lett. 112, 067201 (2014).].