Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states

TL;DR

This paper develops an algebraic framework to find exact nonequilibrium steady states in open integrable fermionic quantum systems using graded Yangians and matrix-product operators.

Contribution

It introduces a unifying algebraic approach leveraging graded Yangians to derive exact steady states in boundary-driven fermionic models.

Findings

Exact steady-state density matrices expressed as graded matrix-product operators.

Solutions factorize via vacuum analogues of Baxter's Q-operators.

Framework applies to models with higher-rank symmetries.

Abstract

Using the Lindblad master equation approach, we investigate the structure of steady-state solutions of open integrable quantum lattice models, driven far from equilibrium by incoherent particle reservoirs attached at the boundaries. We identify a class of boundary dissipation processes which permits to derive exact steady-state density matrices in the form of graded matrix-product operators. All the solutions factorize in terms of vacuum analogues of Baxter's Q-operators which are realized in terms of non-unitary representations of certain finite dimensional subalgebras of graded Yangians. We present a unifying framework which allows to solve fermionic models and naturally incorporates higher-rank symmetries. This enables to explain underlying algebraic content behind most of the previously-found solutions.