Analysis of continuous and discrete Wigner approximations for spin dynamics

TL;DR

This paper compares continuous and discrete Wigner approximations for spin dynamics, revealing that both methods initially underestimate correlations along one direction, with implications for modeling quantum spin systems.

Contribution

It introduces a comprehensive comparison of Wigner approximations for spin models, utilizing a geometric correlation matrix visualization to analyze their accuracy.

Findings

Both approximations suppress correlations along one direction at short times.

The comparison provides insights into the limitations of Wigner methods for spin dynamics.

The geometric visualization aids in understanding correlation discrepancies.

Abstract

We compare the continuous and discrete truncated Wigner approximations of various spin models' dynamics to exact analytical and numerical solutions. We account for all components of spin-spin correlations on equal footing, facilitated by a recently introduced geometric correlation matrix visualization technique [R. Mukherjee {\em et al.}, Phys. Rev. A {\bf 97}, 043606 (2018)]. We find that at modestly short times, the dominant error in both approximations is to substantially suppress spin correlations along one direction.