Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques

TL;DR

This paper introduces a phase-space method using SU(2) coherent states to efficiently simulate the quantum dynamics of many-body spin systems, improving scalability and extending simulation times.

Contribution

The authors develop an exact phase-space representation for spin dynamics that outperforms previous methods and applies to frustrated systems in any dimension.

Findings

Linear scaling of numerical effort with system size

Extended simulation times through extrapolation techniques

Successful simulation of quenches in 1D and 2D transverse field Ising models

Abstract

We reformulate the full quantum dynamics of spin systems using a phase space representation based on SU(2) coherent states which generates an exact mapping of the dynamics of any spin system onto a set of stochastic differential equations. The new representation is superior in practice to an earlier phase space approach based on Schwinger bosons, with the numerical effort scaling only linearly with system size. By also implementing extrapolation techniques from quasiclassical equations to the full quantum limit, we are able to extend useful simulation times several fold. This approach is applicable in any dimension including cases where frustration is present in the spin system. The method is demonstrated by simulating quenches in the transverse field Ising model in one and two dimensions