Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions

TL;DR

This paper uncovers a hidden time-reversal symmetry in driven XXZ spin chains, leading to exact solutions, a novel dissipative phase transition, and complex steady-state behaviors including fractal magnetization dependence.

Contribution

It reveals a subtle time-reversal symmetry in driven XXZ models, providing exact solutions and identifying a new dissipative phase transition absent in closed systems.

Findings

Exact solutions for steady states of driven XXZ chains.

Identification of a continuous dissipative phase transition.

Discovery of fractal dependence of magnetization on interaction strength.

Abstract

We show that several models of interacting XXZ spin chains subject to boundary driving and dissipation possess a subtle kind of time-reversal symmetry, making their steady states exactly solvable. We focus on a model with a coherent boundary drive, showing that it exhibits a unique continuous dissipative phase transition as a function of the boundary drive amplitude. This transition has no analogue in the bulk closed system, or in incoherently driven models. We also show the steady state magnetization exhibits a surprising fractal dependence on interaction strength, something previously associated with less easily measured infinite-temperature transport quantities (the Drude weight). Our exact solution also directly yields driven-dissipative double-chain models that have pure, entangled steady states that are also current carrying.