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We present a formalism for simulating quantum dynamics of lattice spin-onesystems by first introducing local hidden variables and then doingsemiclassical (truncated Wigner) approximation in the extended phase space. Inthis way we exactly take into account the local on-site Hamiltonian andapproximately treat spin-spin interactions. In particular, we represent eachspin with eight classical SU(3) variables. Three of them represent the usualspin components and five others are hidden variables representing localspin-spin correlations. We compare our formalism with exact quantum dynamics offully connected spin systems and find very good agreement. As an application wediscuss quench dynamics of a Bose-Hubbard model near the superfluid-insulatortransition for a 3D lattice system consisting of 1000 sites.

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