Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models

TL;DR

This paper evaluates the cluster Truncated Wigner Approximation (cTWA) for disordered Heisenberg spin chains, demonstrating its high accuracy with optimal clustering strategies and introducing a new initial sampling scheme to improve computational efficiency.

Contribution

It introduces a clustering strategy inspired by SDRG for cTWA and develops a discrete sampling scheme for the initial Wigner function, enhancing accuracy and efficiency.

Findings

cTWA yields highly accurate results across parameters.

Cluster choice based on SDRG improves accuracy, especially in strong disorder.

The new sampling scheme reduces Monte Carlo noise.

Abstract

We present a comprehensive numerical investigation of the cluster Truncated Wigner Approximation (cTWA) applied to quench dynamics in bond-disordered Heisenberg spin chains with power-law interactions. We find that cTWA yields highly accurate results over a wide parameter range. However, its accuracy hinges on a suitable choice of clusters. By using a clustering strategy inspired by the strong disorder renormalisation group (SDRG)/real-space renormalization group (RSRG), clusters of two spins are sufficient to obtain essentially exact results in the regime of strong disorder. Surprisingly, even for rather weak disorder, e.g.\ in the presence of very long-range interactions, this choice of clustering outperforms a naive choice of clusters of consecutive spins. Additionally, we develop a discrete sampling scheme for the initial Wigner function, as an alternative to the originally introduced scheme based on Gaussian approximations. This sampling scheme puts cTWA on the same conceptional footing as regular dTWA for single spins and yields some reduction in the Monte Carlo shot noise compared to the Gaussian scheme.