Expansion Dynamics in the One-Dimensional Fermi-Hubbard Model

Expansion dynamics of interacting fermions in a lattice is simulated within the one-dimensional (1D) Hubbard model, using the essentially exact time-evolving block decimation (TEBD) method. In particular, the expansion of an initial band-insulator state is considered. We analyze the simulation results based on the dynamics of a two-site two-particle system, the so-called Hubbard dimer. Our findings describe essential features of a recent experiment on the expansion of a Fermi gas in a two-dimensional lattice. We show that the Hubbard-dimer dynamics, combined with a two-fluid model for the paired and nonpaired components of the gas, gives an efficient description of the full dynamics. This should be useful for describing dynamical phenomena of strongly interacting Fermions in a lattice in general.