# A generalized phase space approach for solving quantum spin dynamics

## TL;DR

The paper introduces GDTWA, a new semi-classical phase-space sampling method for simulating quantum spin dynamics in large, interacting lattice systems with arbitrary spin, capturing complex thermalization and entanglement phenomena.

## Contribution

It presents GDTWA, a novel numerical approach that accurately models quantum spin dynamics beyond mean-field approximations for large, high-spin systems with long-range interactions.

## Key findings

- GDTWA accurately reproduces short- and long-time dynamics.
- The method captures quantum-thermalization effects.
- Large S systems can exhibit greater entanglement than S=1/2 systems.

## Abstract

Numerical techniques to efficiently model out-of-equilibrium dynamics in interacting quantum many-body systems are key for advancing our capability to harness and understand complex quantum matter. Here we propose a new numerical approach which we refer to as GDTWA. It is based on a discrete semi-classical phase-space sampling and allows to investigate quantum dynamics in lattice spin systems with arbitrary $S\geq 1/2$. We show that the GDTWA can accurately simulate dynamics of large ensembles in arbitrary dimensions. We apply it for $S>1/2$ spin-models with dipolar long-range interactions, a scenario arising in recent experiments with magnetic atoms. We show that the method can capture beyond mean-field effects, not only at short times, but it also correctly reproduces long time quantum-thermalization dynamics. We benchmark the method with exact diagonalization in small systems, with perturbation theory for short times, and with analytical predictions made for closed system which feature quantum-thermalization at long times. By computing the Renyi entropy, currently an experimentally accessible quantifier of entanglement, we reveal that large $S$ systems can feature larger entanglement than corresponding $S=1/2$ systems. Our analyses demonstrate that the GDTWA can be a powerful tool for modeling complex spin dynamics in regimes where other state-of-the art numerical methods fail.