Nonequilibrium phases and phase transitions of the XY-model

TL;DR

This paper maps the non-equilibrium phase diagram of a transverse field XY spin chain coupled to reservoirs, revealing generic mixed-order transitions and analyzing their properties through correlation functions and entanglement measures.

Contribution

It provides the first comprehensive analysis of non-equilibrium phases and mixed-order transitions in the XY model with open quantum system dynamics.

Findings

Identification of non-equilibrium phases via correlation functions and entanglement

Analytical determination of critical exponents for mixed-order transitions

Comparison of non-Markovian and Markovian reservoir effects

Abstract

We obtain the steady-state phase diagram of a transverse field XY spin chain coupled at its ends to magnetic reservoirs held at different magnetic potentials. In the long-time limit, the magnetization bias across the system generates a current-carrying non-equilibrium steady-state. We characterize the different non-equilibrium phases as functions of the chain's parameters and magnetic potentials, in terms of their correlation functions and entanglement content. The mixed-order transition, recently observed for the particular case of a transverse field Ising chain, is established to emerge as a generic out-of-equilibrium feature and its critical exponents are determined analytically. Results are also contrasted with those obtained in the limit of Markovian reservoirs. Our findings should prove helpful in establishing the properties of non-equilibrium phases and phase transitions of extended open quantum systems.