Non-equilibrium phase transition in a periodically driven XY spin chain

TL;DR

This paper develops a Floquet state formulation for periodically driven open fermionic systems and applies it to an XY spin chain, revealing complex phase diagrams with re-entrant phases and long-range correlations.

Contribution

It introduces a Lyapunov equation approach to analyze Floquet states in open quantum systems and applies it to a driven XY spin chain with novel phase behavior.

Findings

Re-entrant phases of long-range correlations identified

Complex phase diagram mapped via Floquet quasi-particle dispersion

Method applicable to a broad class of periodically driven open systems

Abstract

We present a general formulation of Floquet states of periodically time-dependent open Markovian quasi-free fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicekd XY spin 1/2 chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with re-entrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting non-trivial stationary points of Floquet quasi-particle dispersion relation.