Dynamics of finite Fermi-Hubbard and Bose-Hubbard systems

This paper analyzes dynamical properties of small Fermi-Hubbard and Bose-Hubbard systems, focusing on the structure of the underlying Hilbert space. We evaluate time-dependent quantities such as the return probability to the initial state and the spin imbalance of spin-1/2 fermions. The results are compared with recent experimental observations in ultracold gases. For the symmetric two-site Fermi-Hubbard model we find that the spin imbalance and the return probability are controlled by two and three frequencies, respectively. The spin imbalance and the return probability are identical for the asymmetric Falicov-Kimball limit and controlled by only one frequency. In general, the transition probabilities between the initial state and energy eigenstates depend strongly on the particle-particle interaction. This is discussed for "self trapping" of spinless bosons in a double-well potential. We observe that the available Hilbert space is reduced significantly by strong interaction.