Energy dependence of localization with interactions and disorder: The generalized inverse participation ratio of an ensemble of two-site Anderson-Hubbard systems

Abstract

After Anderson's prediction of disorder-induced insulating behavior, extensive work found no singularities in the density of states of localized systems. However, Johri and Bhatt recently uncovered the existence of a non-analyticity in the density of states near the band edge of non-interacting systems with bounded disorder, in an energy range outside that captured by previous work. Moreover, this feature marks the boundary of an energy range in which the localization is sharply suppressed. Given strong current interest in the effect of interactions on disordered systems, we explore here the effect of a Hubbard $U$ interaction on this behavior. We find that in ensembles of small systems a cusp in the density of states persists and continues to be associated with a sharp suppression of the localization. We explore the origins of this behavior and discuss its connection with many-body localization.

6 pages, 3 figures

References in corpus (7)

• Phenomenology of fully many-body-localized systems
• Many-body localization in a disordered quantum Ising chain
• Metal-insulator transition in two-dimensional electron systems
• Spectral features of a many-body localized system weakly coupled to a heat bath
• Dynamical Mean Field Study of the Two-Dimensional Disordered Hubbard Model
• Dependence of decoherence-assisted classicality on the ways a system is partitioned into subsystems
• Self-consistent study of Anderson localization in the Anderson-Hubbard model in two and three dimensions

Cited by in corpus (7)

• Local integrals of motion in the two-site Anderson-Hubbard model
• Hubbard pair cluster in the external fields. Studies of the magnetic properties
• Nonequilibrium charge transport through Falicov-Kimball structures connected to metallic leads
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• Finite temperature phase diagram of the extended Bose-Hubbard model in the presence of disorder
• Persistence of energy-dependent localization in the Anderson-Hubbard model with increasing system size and doping