arXiv:2004.03506 · Physical Review Research

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

Filippo Stellin, Giuliano Orso

Published Sep 28, 2020• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.033501

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Two-body mobility edge in the Anderson-Hubbard model: molecular versus scattering states

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arXiv:2004.03506 · Physical Review Research

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

Filippo Stellin, Giuliano Orso

Published Sep 28, 2020• 5 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevresearch.2.033501

Related papers

Two-body mobility edge in the Anderson-Hubbard model: 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 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 metal-insulator transitions in the Anderson-Hubbard model

Filippo Stellin, Giuliano Orso

Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.Abstract We review our recent results on Anderson localization in systems of two interacting particles coupled by contact interactions. Based on an exact mapping to an effective single-particle problem, we numerically investigate the occurrence of metal-insulator phase transitions for the pair in two-(2D) and three-dimensional (3D) disordered lattices. In two dimensions, we find that interactions cause an exponential enhancement of the pair localization length with respect to its single-particle counterpart, but do not induce a delocalization transition. In particular we show that previous claims of 2D interaction-induced Anderson transitions are the results of strong finite-size effects. In three dimensions we find that the pair undergoes a metal-insulator transition belonging to the same (orthogonal) universality class of the noninteracting model. We then explore the phase diagram in the space of energy E, disorder W and interaction strength U, which reveals a rich and counterintuitive structure, endowed with multiple metallic and insulating phases. We point out that this phenomenon originates from the molecular and scattering-like nature of the pair states available at given energy and disorder strength.

arXiv:2012.01103Journal of Physics Conference SeriesJan 1, 20210 citations

Absence of two-body delocalization transitions in the two-dimensional Anderson-Hubbard model

Filippo Stellin, Giuliano Orso

We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find that all pair states are localized in lattices of infinite size. In particular, we show that previous claims of an interaction-induced mobility edge are biased by severe finite-size effects. The localization length of a pair with zero total energy exhibits a nonmonotonic behavior as a function of the interaction strength, characterized by an exponential enhancement in the weakly interacting regime. Our findings also suggest that the many-body mobility edge of the 2D Anderson-Hubbard model disappears in the zero-density limit, irrespective of the (bosonic or fermionic) quantum statistics of the particles.We investigate Anderson localization of two particles moving in a two-dimensional (2D) disordered lattice and coupled by contact interactions. Based on transmission-amplitude calculations for relatively large strip-shaped grids, we find that all pair states are localized in lattices of infinite size. In particular, we show that previous claims of an interaction-induced mobility edge are biased by severe finite-size effects. The localization length of a pair with zero total energy exhibits a nonmonotonic behavior as a function of the interaction strength, characterized by an exponential enhancement in the weakly interacting regime. Our findings also suggest that the many-body mobility edge of the 2D Anderson-Hubbard model disappears in the zero-density limit, irrespective of the (bosonic or fermionic) quantum statistics of the particles.

arXiv:2007.10708Physical review. B./Physical review. BOct 13, 20204 citations

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The localization properties of quasiparticle pairs above a frozen Fermi sea in the two- and three-dimensional Anderson model with Hubbard interaction are investigated. The dependence of the width Γ of the local spectral density on the pair excitation energy ε2, the disorder W, the interaction strength U and the linear system size L is determined. The obtained results allow to emphasize an interaction-induced pair delocalization effect even when the quasiparticles remain individually localized. The corresponding mobility edge is further estimated and the disorder versus interaction phase diagram is determined. Further investigations focusing on the spectral properties of the system and the transition from Poisson to Wigner-Dyson statistics corroborate these conclusions. The relevance of this effect with respect to the one-quasiparticle lifetime is finally discussed.The localization properties of quasiparticle pairs above a frozen Fermi sea in the two- and three-dimensional Anderson model with Hubbard interaction are investigated. The dependence of the width Γ of the local spectral density on the pair excitation energy ε2, the disorder W, the interaction strength U and the linear system size L is determined. The obtained results allow to emphasize an interaction-induced pair delocalization effect even when the quasiparticles remain individually localized. The corresponding mobility edge is further estimated and the disorder versus interaction phase diagram is determined. Further investigations focusing on the spectral properties of the system and the transition from Poisson to Wigner-Dyson statistics corroborate these conclusions. The relevance of this effect with respect to the one-quasiparticle lifetime is finally discussed.

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Mobility edge of two interacting particles in three-dimensional random potentials

Filippo Stellin, Giuliano Orso

We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength $U$ . The two-body problem is exactly mapped into an effective single-particle equation for the center-of-mass motion, whose localization properties are studied numerically. We show that, for zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized. In particular, the critical disorder strength exhibits a nonmonotonic behavior as a function of $|U|$ , increasing sharply for weak interactions and converging to a finite value in the strong-coupling limit. Within our numerical accuracy, short-range interactions do not affect the universality class of the transition.We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength $U$. The two-body problem is exactly mapped into an effective single-particle equation for the center-of-mass motion, whose localization properties are studied numerically. We show that, for zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized. In particular, the critical disorder strength exhibits a nonmonotonic behavior as a function of $|U|$, increasing sharply for weak interactions and converging to a finite value in the strong-coupling limit. Within our numerical accuracy, short-range interactions do not affect the universality class of the transition.

arXiv:1903.06214Physical review. B./Physical review. BJun 28, 20195 citations

Metal-insulator transition in a weakly interacting disordered electron system

Chinedu E. Ekuma, Shuxiang Yang, Hanna Terletska +4 more

The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, nonlocal cluster self-energy $[{\mathrm{\ensuremath{\Sigma}}}_{c}[\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{G}}](i,j\ensuremath{\ne}i)]$ up to second order in the perturbation expansion of interactions, ${U}^{2}$ , with a systematic incorporation of nonlocal spatial correlations and diagonal disorder, we explore the initial effects of electron interactions ( $U$ ) in three dimensions. We find that the critical disorder strength ( ${W}_{c}^{U}$ ), required to localize all states, increases with increasing $U$ ; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate $W$ close to ${W}_{c}^{U}$ and demonstrate that the mobility edge (${\ensuremath{\omega}}_{\ensuremath{\epsilon}}$) is preserved as long as the chemical potential, $\ensuremath{\mu}$, is at or beyond the mobility edge energy.The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, nonlocal cluster self-energy $[{\mathrm{\ensuremath{\Sigma}}}_{c}[\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{G}}](i,j\ensuremath{\ne}i)]$ up to second order in the perturbation expansion of interactions, ${U}^{2}$, with a systematic incorporation of nonlocal spatial correlations and diagonal disorder, we explore the initial effects of electron interactions ($U$) in three dimensions. We find that the critical disorder strength (${W}_{c}^{U}$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate $W$ close to ${W}_{c}^{U}$ and demonstrate that the mobility edge (${\ensuremath{\omega}}_{\ensuremath{\epsilon}}$) is preserved as long as the chemical potential, $\ensuremath{\mu}$, is at or beyond the mobility edge energy.

arXiv:1503.00025Physical Review BNov 25, 201519 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.

We investigate Anderson transitions for a system of two particles moving in a three-dimensional disordered lattice and subject to on-site (Hubbard) interactions of strength

U

. The two-body problem is exactly mapped into an effective single-particle equation for the center-of-mass motion, whose localization properties are studied numerically. We show that, for zero total energy of the pair, the transition occurs in a regime where all single-particle states are localized. In particular, the critical disorder strength exhibits a nonmonotonic behavior as a function of

|U|

, increasing sharply for weak interactions and converging to a finite value in the strong-coupling limit. Within our numerical accuracy, short-range interactions do not affect the universality class of the transition.

{U}^{2}

, with a systematic incorporation of nonlocal spatial correlations and diagonal disorder, we explore the initial effects of electron interactions (

U

) in three dimensions. We find that the critical disorder strength (

{W}_{c}^{U}

), required to localize all states, increases with increasing

U

; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate

W

close to

{W}_{c}^{U}

and demonstrate that the mobility edge (${\ensuremath{\omega}}_{\ensuremath{\epsilon}}$) is preserved as long as the chemical potential, $\ensuremath{\mu}$, is at or beyond the mobility edge energy.