Optimal time-dependent lattice models for nonequilibrium dynamics

Lattice models are central to the physics of ultracold atoms and condensed matter. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study an interaction quench scenario involving higher bands. We find a separation of time-scales in the dynamics. The results are compared with numerically exact results of the time-dependent many-body Schrödinger equation. We thereby show that—under some circumstances—the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.