Hole dynamics in one-dimensional optical lattices

Abstract

We study the dynamical properties of a single hole on top of a Mott insulator described by the Bose-Hubbard Hamiltonian in the strongly interacting regime. The full Hamiltonian can be mapped to an effective one by means of the perturbation theory approach, which allows us to obtain the hole effective mass and study the long-time dynamics of a hole, initially localized with a Gaussian distribution or a delta function. The hole effective mass becomes infinite at a critical value of the onsite interaction, which is reflected in its time evolution described by a dispersionless Gaussian distribution. Moreover, a hole, initially localized in a single site, exhibits an oscillatory behavior in its time evolution. We also perform exact diagonalization simulations of the full Bose-Hubbard model and compare the results with the predictions obtained with perturbation theory. The hole effective mass shows a similar trend in the strong coupling regime as in our perturbation theory, however, it does not diverge at a critical on-site interaction. Nevertheless, we also obtain an oscillatory behavior of the hole density in time when starting the time evolution with a hole localized in a site.