  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.
