Fragile fate of driven-dissipative XY phase in two dimensions

TL;DR

This paper investigates the stability of XY phases in two-dimensional driven-dissipative bosonic systems, revealing that while an equilibrium-like phase can emerge, it is inherently fragile and susceptible to symmetry-breaking and disorder effects.

Contribution

It demonstrates the emergence of an effectively equilibrium XY phase in a driven-dissipative system and analyzes its instability due to non-equilibrium perturbations.

Findings

An equilibrium-like XY phase can appear in driven-dissipative 2D systems.

The XY phase is protected by a ${ m Z}_2$ symmetry but remains unstable.

Non-equilibrium perturbations introduce relevant directions in RG flow.

Abstract

Driven-dissipative systems define a broad class of non-equilibrium systems where an external drive (e.g. laser) competes with a dissipative environment. The steady state of dynamics is generically distinct from a thermal state characteristic of equilibrium. As a representative example, a driven-dissipative system with a continuous symmetry is generically disordered in two dimensions in contrast with the well-known algebraic order in equilibrium XY phases. In this paper, we study a 2D driven-dissipative model of weakly interacting bosons with a continuous $U(1)$ symmetry. Our aim is two-fold: First, we show that an effectively equilibrium XY phase emerges despite the driven nature of the model, and that it is protected by a natural ${\mathbb Z}_2$ symmetry of the dynamics. Second, we argue that this phase is unstable against symmetry-breaking perturbations as well as static disorder, whose mechanism in most cases has no analog in equilibrium. In the language of renormalization group theory, we find that, outside equilibrium, there are more relevant directions away from the XY phase.