Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

Abstract

Most of our quantitative understanding of disorder-induced metal-insulator transitions comes from numerical studies of simple noninteracting tight-binding models, like the Anderson model in three dimensions. An important outstanding problem is the fate of the Anderson transition in the presence of additional Hubbard interactions of strength U between particles. Based on large-scale numerics, we compute the position of the mobility edge for a system of two identical bosons or two fermions with opposite spin components. The resulting phase diagram in the interaction-energy-disorder space possesses a remarkably rich and counterintuitive structure, with multiple metallic and insulating phases. We show that this phenomenon originates from the molecular or scatteringlike nature of the pair states available at given energy E and disorder strength W. The disorder-averaged density of states of the effective model for the pair is also investigated. Finally, we discuss the implications of our results for ongoing research on many-body localization.

Two-body metal-insulator transitions in the Anderson-Hubbard model

“…3 show that the crossing points have completely disappeared, suggesting that the pair localizes in an infinite lattice, irrespectively of the specific value of U . We therefore conclude that the former results [27,28] were plagued by severe finitesize effects, due to the limited system sizes accessible at that time, and no Anderson transition can take [32]. The orange triangles data refer to the phase boundary at E = 0, calculated in Ref.…”

“…Making J explicit, in the strongly interacting regime, that corresponds to E ∼ U with |E| ≫ W, J, the effective Hamiltonian takes the same form of the single-particle Anderson model, but endowed with modified parameters, describing the motion of tightly bound pairs [34,32]…”

“…3 correspond to configurations unaccessible to the system, where the density of state is exactly zero. These regions are limited by the black dashed curves, corresponding to the rigorous band edges, which have been calculated analytically [32].…”

“…In this proceeding article, we review our recent numerical works [31,32,33] on two-body Anderson localization in two and in three spatial dimensions, by highlighting the most important results.…”

“…Inset: disorder-averaged density of states ρ K of the effective Hamiltonian of the pair calculated for W = 23.5 using a cubic grid of sizes L = M = 20 with periodic boundary conditions. (b) Phase diagram for a pair with total energy E = U (blue circles data)[32]. The orange triangles data refer to the phase boundary at E = 0, calculated in Ref [31],.…”