Cluster truncated Wigner approximation for bond-disordered Heisenberg spin models

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.

16 pages, 13 figures, submitted to Phys. Rev. B

References in corpus (11)

• The density-matrix renormalization group in the age of matrix product states
• Probing many-body dynamics on a 51-atom quantum simulator
• Real time evolution using the density matrix renormalization group
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Time-evolving a matrix product state with long-ranged interactions
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Quantum criticality of hot random spin chains
• Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Pair localization in dipolar systems with tunable positional disorder