Open quantum spin chains with non-reciprocity: a theoretical approach based on the time-dependent generalized Gibbs ensemble

TL;DR

This paper develops a theoretical framework using the time-dependent generalized Gibbs ensemble to analyze non-reciprocal open quantum spin chains, accurately predicting their dynamics and revealing relations between magnetization and current.

Contribution

It introduces a novel theoretical approach for non-reciprocal quantum spin chains that extends beyond non-interacting fermion models, with validated numerical benchmarking.

Findings

Accurate characterization of spin chain dynamics via rapidity distribution.

Derivation of coupled differential equations for system evolution.

Insights into magnetization-current relations and power-law exponents.

Abstract

We study an open quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble. In the regime of weak dissipation the system is fully characterized by its rapidity distribution and we derive a closed set of coupled differential equations governing their time evolution. We check the accuracy of this theory by benchmarking the results against numerical simulations. Using this framework we are able to compute both the magnetization density and current dynamics, identifying some relations between the two. The problem of the anomalous power-law exponents identified in a previous work is discussed. Our work constitutes a theoretical approach that is able to describe the physics of non-reciprocal open quantum spin chains beyond analyses based on non-interacting fermions.