  Boson lattices are theoretically well described by the Hubbard model. The
basic model and its variants can be effectively simulated using Monte Carlo
techniques. We describe two newly developed approaches, the Stochastic Series
Expansion (SSE) with directed loop updates and continuous--time Diffusion Monte
Carlo (CTDMC). SSE is a formulation of the finite temperature partition
function as a stochastic sampling over product terms. Directed loops is a
general framework to implement this stochastic sampling in a non--local fashion
while maintaining detailed balance. CTDMC is well suited to finding exact
ground--state properties, applicable to any lattice model not suffering from
the sign problem; for a lattice model the evolution of the wave function can be
performed in continuous time without any time discretization error. Both the
directed loop algorithm and the CTDMC are important recent advances in
development of computational methods. Here we present results for a Hubbard
model for anti--ferromagnetic spin--1 bosons in one dimensions, and show
evidence for a dimerized ground state in the lowest Mott lobe.
