Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1507.04289 · Physical Review B

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

Jayanayana Perera, Rachel Wortis

Published Aug 6, 2015• 8 citations
arXivHTMLPDF

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 [Phys. Rev. Lett. 109, 076402 (2012) and Phys. Rev. B 86, 125140 (2012)] recently uncovered the existence of a nonanalyticity in the density of states near the band edge of noninteracting 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.

DOI
10.1103/physrevb.92.085110

Related papers

Persistence of energy-dependent localization in the Anderson–Hubbard model with increasing system size and doping

P Daley, R Wortis

Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson-Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states.

arXiv:1601.03010•Journal of Physics Condensed Matter•Mar 29, 2016•0 citations

Correlating density of states features with localization strength in disordered interacting systems

Jayanayana Perera

Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified. Author Keywords: Correlated electrons, Disorder, Localization

•Jan 1, 2015•0 citations

Temperature dependence of the zero-bias anomaly in the Anderson–Hubbard model: insights from an ensemble of two-site systems

Rachel Wortis, W. A. Atkinson

Motivated by experiments on doped transition metal oxides, this paper considers the interplay of interactions, disorder, kinetic energy and temperature in a simple system. An ensemble of two-site Anderson-Hubbard model systems has already been shown to display a zero-bias anomaly (Wortis and Atkinson 2010 Phys. Rev. B 82 073107) which shares features with that found in the two-dimensional Anderson-Hubbard model (Chiesa et al 2008 Phys. Rev. Lett. 101 086401). Here the temperature dependence of the density of states of this ensemble is examined. In the atomic limit, there is no zero-bias anomaly at zero temperature, but one develops at small nonzero temperatures. With hopping, small temperatures augment the zero-temperature kinetic-energy-driven zero-bias anomaly, while at larger temperatures the anomaly is filled in.

arXiv:1008.2245•Journal of Physics Condensed Matter•Feb 17, 2011•6 citations

Interplay of Anderson localization and strong interactions in disordered systems

Peter Henseler

We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.

•Jan 1, 2009•0 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.

arXiv:2004.03506•Physical Review Research•Sep 28, 2020•5 citations

Physical mechanism for a kinetic energy driven zero-bias anomaly in the Anderson-Hubbard model

Rachel Wortis, W. A. Atkinson

The combined effects of strong disorder, strong correlations, and hopping in the Anderson-Hubbard model have been shown to produce a zero-bias anomaly which has an energy scale proportional to the hopping and minimal dependence on interaction strength, disorder strength, and doping. Disorder-induced suppression of the density of states for a purely local interaction is inconsistent with both the Efros-Shklovskii Coulomb gap and the Altshuler-Aronov anomaly, and moreover the energy scale of this anomaly is inconsistent with the standard energy scales of both weak- and strong-coupling pictures. We demonstrate that a density of states anomaly with similar features arises in an ensemble of two-site systems, and we argue that the energy scale $t$ emerges in strongly correlated systems with disorder due to the mixing of lower and upper Hubbard orbitals on neighboring sites.

arXiv:1004.3309•Physical Review B•Aug 31, 2010•13 citations
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 [Phys. Rev. Lett. 109, 076402 (2012) and Phys. Rev. B 86, 125140 (2012)] recently uncovered the existence of a nonanalyticity in the density of states near the band edge of noninteracting 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 UUU 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.
Non-interacting systems with bounded disorder have been shown to exhibit sharp density of state peaks at the band edge which coincide with an energy range of abruptly suppressed localization. Recent work has shown that these features also occur in the presence of on-site interactions in ensembles of two-site Anderson-Hubbard systems at half filling. Here we demonstrate that this effect in interacting systems persists away from half filling, and moreover that energy regions with suppressed localization continue to appear in ensembles of larger systems despite a loss of sharp features in the density of states.
Johri and Bhatt found singular behavior near the band edge in the density of states as well as in the inverse participation ratio of the Anderson model. These singularities mark a transition to an energy range dominated by resonant states. We study the interacting case using an ensemble of two-site Anderson-Hubbard systems. We find the ensemble-averaged density of states and generalized inverse participation ratio have more structure than in the non-interacting case because there are more transitions and in particular the transitions depend on the ground state. Nonetheless, there are regions of sharp decline in the generalized inverse participation ratio associated with specific density of state features. Moreover these features move closer to the Fermi level with the addition of interactions making them more experimentally accessible. Unfortunately resonances unique to interacting systems cannot be specifically identified. Author Keywords: Correlated electrons, Disorder, Localization
Motivated by experiments on doped transition metal oxides, this paper considers the interplay of interactions, disorder, kinetic energy and temperature in a simple system. An ensemble of two-site Anderson-Hubbard model systems has already been shown to display a zero-bias anomaly (Wortis and Atkinson 2010 Phys. Rev. B 82 073107) which shares features with that found in the two-dimensional Anderson-Hubbard model (Chiesa et al 2008 Phys. Rev. Lett. 101 086401). Here the temperature dependence of the density of states of this ensemble is examined. In the atomic limit, there is no zero-bias anomaly at zero temperature, but one develops at small nonzero temperatures. With hopping, small temperatures augment the zero-temperature kinetic-energy-driven zero-bias anomaly, while at larger temperatures the anomaly is filled in.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
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.
The combined effects of strong disorder, strong correlations, and hopping in the Anderson-Hubbard model have been shown to produce a zero-bias anomaly which has an energy scale proportional to the hopping and minimal dependence on interaction strength, disorder strength, and doping. Disorder-induced suppression of the density of states for a purely local interaction is inconsistent with both the Efros-Shklovskii Coulomb gap and the Altshuler-Aronov anomaly, and moreover the energy scale of this anomaly is inconsistent with the standard energy scales of both weak- and strong-coupling pictures. We demonstrate that a density of states anomaly with similar features arises in an ensemble of two-site systems, and we argue that the energy scale ttt emerges in strongly correlated systems with disorder due to the mixing of lower and upper Hubbard orbitals on neighboring sites.