SU(3) semiclassical representation of quantum dynamics of interacting spins

TL;DR

This paper introduces a semiclassical SU(3) phase space approach for simulating quantum dynamics of interacting spin-one systems, accurately capturing local Hamiltonian effects and approximating spin-spin interactions.

Contribution

It develops a novel SU(3) semiclassical formalism with hidden variables to model quantum spin dynamics, improving on existing methods.

Findings

Excellent agreement with exact quantum dynamics in test cases

Effective simulation of large 3D lattice systems with 1000 sites

Captures local Hamiltonian effects accurately

Abstract

We present a formalism for simulating quantum dynamics of lattice spin-one systems by first introducing local hidden variables and then doing semiclassical (truncated Wigner) approximation in the extended phase space. In this way we exactly take into account the local on-site Hamiltonian and approximately treat spin-spin interactions. In particular, we represent each spin with eight classical SU(3) variables. Three of them represent the usual spin components and five others are hidden variables representing local spin-spin correlations. We compare our formalism with exact quantum dynamics of fully connected spin systems and find very good agreement. As an application we discuss quench dynamics of a Bose-Hubbard model near the superfluid-insulator transition for a 3D lattice system consisting of 1000 sites.