Fluctuations and Non-Hermiticity in the Stochastic Approach to Quantum Spins

TL;DR

This paper introduces a stochastic differential equation approach to simulate quantum spin dynamics, enabling larger system sizes and hybrid methods, while analyzing non-Hermitian effects on observable accuracy.

Contribution

It develops a stochastic framework for quantum spin dynamics that scales to larger systems and incorporates hybrid matrix product state techniques.

Findings

Accurately simulates quantum spin dynamics up to 49 spins.

Identifies non-Hermitian effects causing norm growth and observable deviations.

Proposes correction methods for late-time inaccuracies.

Abstract

We investigate the non-equilibrium dynamics of isolated quantum spin systems via an exact mapping to classical stochastic differential equations. We show that one can address significantly larger system sizes than recently obtained, including two-dimensional systems with up to 49 spins. We demonstrate that the results for physical observables are in excellent agreement with exact results and alternative numerical techniques where available. We further develop a hybrid stochastic approach involving matrix product states. In the presence of finite numerical sampling, we show that the non-Hermitian character of the stochastic representation leads to the growth of the norm of the time-evolving quantum state and to departures for physical observables at late times. We demonstrate approaches that correct for this and discuss the prospects for further development.