Non-Equilibrium Quantum Spin Dynamics from Classical Stochastic Processes

TL;DR

This paper develops a stochastic classical approach to analyze non-equilibrium quantum spin dynamics, providing exact formulas and exploring behavior during quantum phase transitions, with implications for numerical simulations.

Contribution

It introduces a broad applicability stochastic method for quantum spin systems, including exact formulas and analysis of dynamical phase transitions, advancing the classical simulation of quantum dynamics.

Findings

Exact formulas for expectation values and correlations post-quench

Analysis of stochastic variables during quantum phase transitions

Growth of fluctuations in classical stochastic description

Abstract

Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development.