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 scattering-like 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.
Highlights
A central concept in the physics of disordered systems is Anderson localization [1], namely the absence of wave diffusion in certain random media as a result of interference effects between the multiple scattering paths generated by the impurities
A natural question that arises from our discussion is: How does the two-body phase diagram in the E − W plane behave in the limit of vanishing interactions? What is the explicit connection with the single-particle mobility edge in the ε − W plane? The answer to this question is shown in Fig. 8, where the data symbols correspond to the critical points at vanishing interactions obtained for E = −15 and E = −12.25 from the numerical data of Fig. 3 and Fig. 5(a)
In this work we have investigated the localization properties of two identical bosons or two fermions with opposite spins moving in a disordered three-dimensional lattice and subject to onsite interactions
Summary
A central concept in the physics of disordered systems is Anderson localization [1], namely the absence of wave diffusion in certain random media as a result of interference effects between the multiple scattering paths generated by the impurities. Of particular interest are many-body mobility edges, namely critical points at finite energy density, separating the many-body localized phase at weak interaction from the metallic, ergodic, phase at strong interaction Evidence of such critical points has been reported [33,34,35,36] in experiments with ultracold atoms in disordered lattices, implementing either the fermionic or the bosonic Anderson-Hubbard model in various dimensions. [76], in this work we investigate pairs with nonzero total energy and map out the phase boundary between localized and extended states in the interaction-energy-disorder space This will be done by considering different cuts of the three-dimensional phase diagram along specific planes. In Appendix B we recall the calculation of the numerical band edge for the (single-particle) Anderson model based on the coherent potential approximation
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