Metastability in an open quantum Ising model

TL;DR

This paper investigates metastability in a dissipative quantum Ising model, revealing long-lived metastable states near phase transitions and linking quantum dynamics to classical stochastic models.

Contribution

It applies a new metastability theory to quantum Ising models, characterizing metastable states and their spectral properties, and connects quantum trajectories to classical stochastic dynamics.

Findings

Identification of long-lived metastable states near phase transition.

Spectral analysis of the quantum master operator reveals metastable manifold.

Quantum trajectories exhibit intermittent dynamics related to metastable phases.

Abstract

We apply a recently developed theory for metastability in open quantum systems to a one-dimensional dissipative quantum Ising model. Earlier results suggest this model features either a non-equilibrium phase transition or a smooth but sharp crossover, where the stationary state changes from paramagnetic to ferromagnetic, accompanied by strongly intermittent emission dynamics characteristic of first-order coexistence between dynamical phases. We show that for a range of parameters close to this transition/crossover point the dynamics of the finite system displays pronounced metastability, i.e., the system relaxes first to long-lived metastable states, before eventual relaxation to the true stationary state. From the spectral properties of the quantum master operator we characterise the low-dimensional manifold of metastable states, which are shown to be probability mixtures of two, paramagnetic and ferromagnetic, metastable phases. We also show that for long times the dynamics can be approximated by a classical stochastic dynamics between the metastable phases that is directly related to the intermittent dynamics observed in quantum trajectories and thus the dynamical phases.