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:cond-mat/9501122 · Journal de Physique I

Enhancement of Persistent Currents by Hubbard Interactions in Disordered 1D Rings: Avoided Level Crossings Interpretation

Michael Kamal, Ziad H. Musslimani, Assa Auerbach

Published Nov 1, 1995• 12 citations
arXivHTMLPDF

Abstract

We study effects of local electron interactions on the persistent current of one dimensional disordered rings. For different realizations of disorder we compute the current as a function of Aharonov-Bohm flux to zeroth and first orders in the Hubbard interaction. We find that the persistent current is {\em enhanced} by onsite interactions. Using an avoided level crossings approach, we derive analytic formulas which explain the numerical results at weak disorder. The same approach also explains the opposite effect (suppression) found for spinless fermion models with intersite interactions.

DOI
10.1051/jp1:1995212

Related papers

Persistent currents of interacting electrons in one-dimensional disordered rings

Wenji Deng, Youyan Liu, Chang-De Gong

We present an exact calculation of the persistent current of electrons with Hubbard interactions in disordered one-dimensional rings. Numerical simulations show that the currents exhibit an interesting dependence on the configuration and strength W of disorder, and the value of the Hubbard interaction U. Our numerical simulations show that disorder and interaction both can monotonically suppress the amplitude of the current. The interaction can sometimes enhance the current of a disordered ring depending on its configuration and degree of disorder, even though smaller than the corresponding ideal-ring value ${\mathit{V}}_{\mathit{F}}$e/L. We have also studied the effect of negative U, and shown that it can influence the current as the positive U does. Based on the eigenvalue theory of a matrix, we give a simple explanation of the effects of disorder and interaction on currents. The main results are consistent with the numerical results for the case of long-range Coulomb interactions.

Physical review. B, Condensed matter•Sep 15, 1994•26 citations

Persistent Currents in Interacting Systems: Role of the Spin

G. Bouzerar, Didier Poilblanc

Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.

Journal de Physique I•Jul 1, 1997•2 citations

Persistent Currents in Interacting Systems: Role of the Spin

G. Bouzerar, Didier Poilblanc

Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is {\it strongly suppressed} by the interaction in the case of spinless fermions while it is {\it significantly enhanced} in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spacial fluctuations of the charge density.

arXiv:cond-mat/9512153•Dec 22, 1995•0 citations

Persistent currents in interacting electronic systems

G. Bouzerar, Didier Poilblanc

Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems. For multichannel systems, a comparative study between models of spinless or spinfull (Hubbard) fermions has been done. First, it is shown that a purely one-dimensional model can not reproduce the correct order of magnitude of the observed currents. For 2D systems, going beyond first order pertubative calculations, we show that the second harmonic of the current is {\it strongly suppressed} in the case of spinless fermion models but {\it significantly enhanced} for the Hubbard model. This reduction (resp. increase) of the second harmonic is related to a strong increase (resp. reduction) of the spacial charge density fluctuations. Our work underlines the important role of the spin degrees of freedom in the persistent currents.

arXiv:cond-mat/9605188•May 30, 1996•0 citations

Effect of electronic interactions on the persistent current in one-dimensional disordered rings

E. Gambetti

The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude of the persistent currents as a function of the boundary conditions for different sets of both interaction and disorder characteristics. In contrast to its noninteracting value, an increase in the stiffness parameter was observed for systems at and off half-filling for weak interactions and nonzero disorders. Within the strong interaction limit, the decrease in stiffness depends on the filling and an analytical approach is developed to recover the observed behaviors. This is required in order to understand its mechanisms. Finally, the study of the localization length confirms the enhancement of the persistent current for moderate interactions when disorders are present at half-filling. Our results reveal two different regimes, one for weak and one for strong interactions at and off half-filling.

arXiv:cond-mat/0501204•Physical Review B•Oct 26, 2005•13 citations

Persistent currents in high dimensions

Jörn Barth, Alexander Altland

We introduce a model for the persistent current carried by spinless fermions moving in a ring with a high-dimensional cross section. The effects of both disorder and electron - electron interaction are considered. It is found that the non-interacting system behaves like previously considered low-dimensional models. The more complicated interacting/disordered case is analysed by means of a functional integral which is evaluated in the limit of infinite dimensionality by expanding in the number of transverse channels. To leading order in this expansion scheme, the Coulomb interaction does not affect the persistent current. It is found that the insensitivity to interaction effects is due to the absence of local contributions to the Coulomb vertex in our model (which in turn is a consequence of the neglect of the electron spin). It is argued that the physical mechanism suppressing the interaction in the high-dimensional spinless model applies to the analogous low-dimensional case as well.

Journal of Physics Condensed Matter•Sep 29, 1997•0 citations
We study effects of local electron interactions on the persistent current of one dimensional disordered rings. For different realizations of disorder we compute the current as a function of Aharonov-Bohm flux to zeroth and first orders in the Hubbard interaction. We find that the persistent current is {\em enhanced} by onsite interactions. Using an avoided level crossings approach, we derive analytic formulas which explain the numerical results at weak disorder. The same approach also explains the opposite effect (suppression) found for spinless fermion models with intersite interactions.
We present an exact calculation of the persistent current of electrons with Hubbard interactions in disordered one-dimensional rings. Numerical simulations show that the currents exhibit an interesting dependence on the configuration and strength W of disorder, and the value of the Hubbard interaction U. Our numerical simulations show that disorder and interaction both can monotonically suppress the amplitude of the current. The interaction can sometimes enhance the current of a disordered ring depending on its configuration and degree of disorder, even though smaller than the corresponding ideal-ring value VF{\mathit{V}}_{\mathit{F}}VF​e/L. We have also studied the effect of negative U, and shown that it can influence the current as the positive U does. Based on the eigenvalue theory of a matrix, we give a simple explanation of the effects of disorder and interaction on currents. The main results are consistent with the numerical results for the case of long-range Coulomb interactions.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is strongly suppressed by the interaction in the case of spinless fermions while it is significantly enhanced in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spatial fluctuations of the charge density.
Persistent currents flowing through disordered mesoscopic rings threaded by a magnetic flux are investigated. Models of fermions with on-site interactions (Hubbard model) or models of spinless fermions with nearest neighbor interactions are considered on 2D cylinders with twisted boundary conditions in one direction to account for a magnetic flux. Self-consistent Hartree-Fock methods are used to treat the electron-electron interaction beyond first order. We show that the second harmonic of the current (which is relevant in the diffusive regime) is {\it strongly suppressed} by the interaction in the case of spinless fermions while it is {\it significantly enhanced} in the Hubbard model. Our data also strongly suggest that the reduction (increase) of this harmonic is related to a strong increase (reduction) of the spacial fluctuations of the charge density.
Persistent currents in disordered mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalization methods in the one-dimensional (1D) case and self-consistent Hartree-Fock treatments for two dimensional (2D) systems. For multichannel systems, a comparative study between models of spinless or spinfull (Hubbard) fermions has been done. First, it is shown that a purely one-dimensional model can not reproduce the correct order of magnitude of the observed currents. For 2D systems, going beyond first order pertubative calculations, we show that the second harmonic of the current is {\it strongly suppressed} in the case of spinless fermion models but {\it significantly enhanced} for the Hubbard model. This reduction (resp. increase) of the second harmonic is related to a strong increase (resp. reduction) of the spacial charge density fluctuations. Our work underlines the important role of the spin degrees of freedom in the persistent currents.
The persistent current is here studied in one-dimensional disordered rings that contain interacting electrons. We used the density matrix renormalization group algorithms in order to compute the stiffness, a measure that gives the magnitude of the persistent currents as a function of the boundary conditions for different sets of both interaction and disorder characteristics. In contrast to its noninteracting value, an increase in the stiffness parameter was observed for systems at and off half-filling for weak interactions and nonzero disorders. Within the strong interaction limit, the decrease in stiffness depends on the filling and an analytical approach is developed to recover the observed behaviors. This is required in order to understand its mechanisms. Finally, the study of the localization length confirms the enhancement of the persistent current for moderate interactions when disorders are present at half-filling. Our results reveal two different regimes, one for weak and one for strong interactions at and off half-filling.
We introduce a model for the persistent current carried by spinless fermions moving in a ring with a high-dimensional cross section. The effects of both disorder and electron - electron interaction are considered. It is found that the non-interacting system behaves like previously considered low-dimensional models. The more complicated interacting/disordered case is analysed by means of a functional integral which is evaluated in the limit of infinite dimensionality by expanding in the number of transverse channels. To leading order in this expansion scheme, the Coulomb interaction does not affect the persistent current. It is found that the insensitivity to interaction effects is due to the absence of local contributions to the Coulomb vertex in our model (which in turn is a consequence of the neglect of the electron spin). It is argued that the physical mechanism suppressing the interaction in the high-dimensional spinless model applies to the analogous low-dimensional case as well.