Non-equilibrium dynamics of Ising models with decoherence: an exact solution

TL;DR

This paper provides an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions under local Markovian decoherence, revealing complex relaxation behaviors and a dynamical phase transition.

Contribution

It introduces a novel exact solution for many-body Ising models with decoherence, uncovering dynamical phase transitions not seen in single-particle models.

Findings

Decoherence influences the relaxation of observables more than single-particle predictions.

A Hopf bifurcation, a dynamical phase transition, is identified in the system.

The results are relevant for quantum information and emulation platforms.

Abstract

The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors. We obtain an exact analytic solution for the non-equilibrium dynamics of Ising models with arbitrary interactions and subject to the most general form of local Markovian decoherence. Our solution shows that decoherence affects the relaxation of observables more than predicted by single-particle considerations. It also reveals a dynamical phase transition, specifically a Hopf bifurcation, which is absent at the single-particle level. These calculations are applicable to ongoing quantum information and emulation efforts using a variety of atomic, molecular, optical, and solid-state systems.