Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

TL;DR

This paper introduces a semiclassical Monte Carlo phase-space method to efficiently simulate quantum spin dynamics in large many-body systems, accurately capturing short-time correlations and entanglement.

Contribution

A novel semiclassical Monte Carlo approach using discrete phase-space sampling for simulating many-body spin dynamics, extending computational capabilities.

Findings

Accurately reproduces short-time correlations and spin squeezing.

Captures entanglement dynamics in large spin systems.

Applicable to regimes inaccessible by other numerical methods.

Abstract

Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science, and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase-space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.