Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach

Finite lattice models are a prototype for interacting quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems have become directly accessible in experiments, including their ultrafast dynamics far from equilibrium. Here, we present a theoretical approach that is able to treat these dynamics in any dimension and fully includes inhomogeneity effects. The method consists in stochastic sampling of mean-field trajectories and is-for not too large two-body interaction strength-found to be much more accurate than time-dependent mean-field at the same order of numerical costs. Furthermore, it can well compete with recent nonequilibrium Green function approaches using second-order Born approximation, which are of substantially larger complexity. The performance of the stochastic mean-field approach is demonstrated for Hubbard clusters with up to 512 particles in one, two, and three dimensions.