Spontaneous symmetry breaking in non-steady modes of open quantum many-body systems

TL;DR

This paper investigates how non-steady eigenmodes in open quantum many-body systems can undergo symmetry-breaking transitions, affecting decoherence dynamics even when the steady state remains unchanged.

Contribution

It introduces the concept of the most coherent eigenmode and demonstrates its phase transition, revealing new insights into non-steady state behavior in open quantum systems.

Findings

Most coherent mode exhibits a phase transition from disordered to ordered phase.

Transition in the most coherent mode affects decoherence of entangled states.

Steady state remains non-singular despite symmetry breaking in eigenmodes.

Abstract

In a quantum many-body system coupled to the environment, its steady state can exhibit spontaneous symmetry breaking when a control parameter exceeds a critical value. In this study, we consider spontaneous symmetry breaking in non-steady modes of an open quantum many-body system. Assuming that the time evolution of the density matrix of the system is described by a Markovian master equation, the dynamics of the system is fully characterized by the eigenmodes and spectrum of the corresponding time evolution superoperator. Among the non-steady eigenmodes with finite lifetimes, we focus on the eigenmodes with the highest frequency, which we call the most coherent mode. For a dissipative spin model, it is shown that the most coherent mode exhibits a transition from a disordered phase to a symmetry-broken ordered phase, even if the steady state does not show singular behavior. We further argue that the phase transition of the most coherent mode induces a qualitative change in the decoherence dynamics of highly entangled states, i.e., the Schr\"odinger's cat states.