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 component. 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 and disorder strength. The behavior of the disorder-averaged density of states of the effective model for the pair is also discussed.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 component. 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 and disorder strength. The behavior of the disorder-averaged density of states of the effective model for the pair is also discussed.

Apr 7, 20200 citations

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

Filippo Stellin, Giuliano Orso

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.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.

arXiv:2004.03506Physical Review ResearchSep 28, 20205 citations

Progress toward the Disordered Hubbard Model

William McGehee, Stanimir Kondov, J. J. Zirbel +1 more

Bulletin of the American Physical SocietyJun 15, 20110 citations

Even-odd correlations in capacitance fluctuations of quantum dots

O. Prus, Assa Auerbach, Yael Aloni +2 more

We investigate effects of short-range interactions on the addition spectra of quantum dots using a disordered Hubbard model. A correlation function S(q) is defined on the inverse compressibility versus filling data, and computed numerically for small lattices. Two regimes of interaction strength are identified: the even/odd fluctuations regime typical of Fermi-liquid ground states, and a regime of structureless S(q) at strong interactions. We propose to understand the latter regime in terms of magnetically correlated localized spins. \textcopyright{} 1996 The American Physical Society.We investigate effects of short-range interactions on the addition spectra of quantum dots using a disordered Hubbard model. A correlation function S(q) is defined on the inverse compressibility versus filling data, and computed numerically for small lattices. Two regimes of interaction strength are identified: the even/odd fluctuations regime typical of Fermi-liquid ground states, and a regime of structureless S(q) at strong interactions. We propose to understand the latter regime in terms of magnetically correlated localized spins. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9607057Physical review. B, Condensed matterNov 15, 199620 citations

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 component. 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 and disorder strength. The behavior of the disorder-averaged density of states of the effective model for the pair is also discussed.