Stochastic Approach to Non-Equilibrium Quantum Spin Systems

TL;DR

This paper presents a stochastic method to analyze non-equilibrium quantum spin systems by transforming quantum dynamics into classical stochastic processes, enabling the study of complex quantum phenomena through classical simulations.

Contribution

The authors develop a unified stochastic framework that links quantum and classical dynamics, allowing analysis of both integrable and non-integrable quantum spin systems in various dimensions.

Findings

Quantum expectation values can be expressed as averages over classical stochastic processes.

Dynamical quantum phase transitions show signatures in classical distribution functions.

The method effectively handles higher-dimensional and non-integrable systems.

Abstract

We investigate a stochastic approach to non-equilibrium quantum spin systems based on recent insights linking quantum and classical dynamics. Exploiting a sequence of exact transformations, quantum expectation values can be recast as averages over classical stochastic processes. We illustrate this approach for the quantum Ising model by extracting the Loschmidt amplitude and the magnetization dynamics from the numerical solution of stochastic differential equations. We show that dynamical quantum phase transitions are accompanied by clear signatures in the associated classical distribution functions, including the presence of enhanced fluctuations. We demonstrate that the method is capable of handling integrable and non-integrable problems in a unified framework, including those in higher dimensions.