The Hubbard Model with Local Disorder in d = ∞

Henry L. Neal

Brandon Leipner-Johns, Rachel Wortis

Although many-body localization has primarily been studied in systems with a single local degree of freedom, experimental studies of many-body localization in cold atom systems motivate exploration of the disordered Hubbard model. With two coupled local degrees of freedom, it is natural to ask how localization in spin relates to disorder in charge and vice versa. Most prior work has addressed disorder in only one of these sectors and often has not used measures of localization which distinguish between charge and spin. Here, we explore localization in the Hubbard model with a wide range of independent values of charge and spin disorder using measures of localization based on charge and spin-specific integrals of motion. Our results demonstrate symmetry between the response of the spin to charge disorder and vice versa, and we find very weak disorder in one channel, so long as the disorder in the other channel is sufficiently strong, results in localization in both channels. The strength of disorder required in the less-disordered channel declines as the system size increases. Furthermore, the weaker the disorder in the less-disordered channel, the longer the timescale at which localization appears in the dynamics of this degree of freedom.

Masaru Sakaida, Kazuto Noda, Norio Kawakami

We study the effects of disorder on an \(s\)-wave superfluid in the attractive Hubbard model using statistical dynamical mean-field theory, which enables us to treat both the correlation effects and the spatial nonuniformity due to disorder in the same framework. The distribution functions of the local density of states and the superfluid order parameter are obtained. From the geometrical average of these quantities, which characterizes the order parameters in disordered systems, we determine the ground-state phase diagram of the attractive Hubbard model with disorder at half-filling and zero temperature. We discuss the superfluid-localization transition and the crossover behavior within the localized phase.

J. H. Drewes, Luke Miller, Eugenio Cocchi +4 more

Masahiko Okumura, S. Yamada, Nobuhiko Taniguchi +1 more

We study an interplay of disorder and correlation in the one-dimensional hole-doped Hubbard-model with disorder (Anderson-Hubbard model) by using the density-matrix renormalization group method. Concentrating on the doped-hole-density profile, we find in a large U/t regime that the clean system exhibits a simple fluidlike behavior whereas finite disorders create locally Mott regions which expand their area with increasing the disorder strength contrary to the conventional sense. We propose that such an anomalous Mott phase formation assisted by disorder is easily observable in atomic Fermi gases by setting up the box-shape trap.