Non-equilibrium spin transport in integrable spin chains: persistent currents and emergence of magnetic domains

TL;DR

This paper constructs exact steady states in the gapless XXZ spin chain, revealing persistent spin currents and magnetic domain formation due to integrability and non-equilibrium dynamics.

Contribution

It introduces a method to evaluate conserved quantities and predicts persistent currents and magnetic domains in integrable spin chains under non-equilibrium conditions.

Findings

Exact steady states for non-equilibrium XXZ chain constructed

Persistent spin currents observed in specific initial states

Magnetic domains grow unboundedly due to interactions

Abstract

We construct exact steady states of unitary non-equilibrium time evolution in the gapless XXZ spin-1/2 chain where integrability preserves ballistic spin transport at long-times. We characterize the quasi-local conserved quantities responsible for this feature and introduce a computationally effective way to evaluate their expectation values on generic matrix product initial states. We employ this approach to reproduce the long-time limit of local observables in all quantum quenches which explicitly break particle-hole or time-reversal symmetry. We focus on a class of initial states supporting persistent spin currents and our predictions remarkably agree with numerical simulations at long times. Furthermore, we propose a protocol for this model where interactions, even when antiferromagnetic, are responsible for the unbounded growth of a macroscopic magnetic domain.