Trajectory-Resolved Weiss Fields for Quantum Spin Dynamics

TL;DR

This paper introduces a trajectory-resolved Weiss field method for simulating quantum spin dynamics, enabling longer and more accurate simulations by capturing sample fluctuations, especially when average fields vanish.

Contribution

It extends previous mean-field sampling techniques by incorporating instantaneous Weiss fields per trajectory, improving simulation accuracy and duration in quantum spin models.

Findings

Enhanced simulation times for quantum spin systems.

Effective in cases with vanishing average Weiss fields.

Connection established to gauge-P phase space approach.

Abstract

We explore the dynamics of quantum spin systems in two and three dimensions using an exact mapping to classical stochastic processes. In recent work we explored the effectiveness of sampling around the mean field evolution as determined by a stochastically averaged Weiss field. Here, we show that this approach can be significantly extended by sampling around the instantaneous Weiss field associated with each stochastic trajectory taken separately. This trajectory-resolved approach incorporates sample to sample fluctuations and allows for longer simulation times. We demonstrate the utility of this approach for quenches in the two-dimensional and three-dimensional quantum Ising model. We show that the method is particularly advantageous in situations where the average Weiss-field vanishes, but the trajectory-resolved Weiss fields are non-zero. We discuss the connection to the gauge-P phase space approach, where the trajectory-resolved Weiss field can be interpreted as a gauge degree of freedom.