Emergence of spontaneous symmetry breaking in dissipative lattice systems

TL;DR

This paper introduces a dynamical theory for spontaneous symmetry breaking in dissipative quantum lattice systems, showing that such systems can have metastable symmetry-breaking states with extensive fluctuations, impacting quantum state preparation.

Contribution

It develops a framework for understanding symmetry breaking in dissipative quantum systems, highlighting the existence of metastable states and limitations in state preparation.

Findings

Existence of metastable symmetry-breaking states in dissipative dynamics.

Dissipative processes satisfying detailed balance cannot uniquely prepare symmetry-broken states.

Implications for quantum simulators and dissipative state engineering.

Abstract

A cornerstone of the theory of phase transitions is the observation that many-body systems exhibiting a spontaneous symmetry breaking in the thermodynamic limit generally show extensive fluctuations of an order parameter in large but finite systems. In this work, we introduce the dynamical analogue of such a theory. Specifically, we consider local dissipative dynamics preparing a steady-state of quantum spins on a lattice exhibiting a discrete or continuous symmetry but with extensive fluctuations in a local order parameter. We show that for all such processes satisfying detailed balance, there exist metastable symmetry-breaking states, i.e., states that become stationary in the thermodynamic limit and give a finite value to the order parameter. We give results both for discrete and continuous symmetries and explicitly show how to construct the symmetry-breaking states. Our results show in a simple way that, in large systems, local dissipative dynamics satisfying detailed balance cannot uniquely and efficiently prepare states with extensive fluctuations with respect to local operators. We discuss the implications of our results for quantum simulators and dissipative state preparation.