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/9411063 · Physical review. B, Condensed matter

Persistent currents in a one-dimensional ring for a disordered Hubbard model

Thierry Giamarchi, B. Sriram Shastry

Published Apr 15, 1995• 146 citations
arXivHTMLPDF

Abstract

We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.

DOI
10.1103/physrevb.51.10915

Related papers

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring

Rudolf A. Römer, Alexander Punnoose

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

arXiv:cond-mat/9505110•Physical review. B, Condensed matter•Nov 15, 1995•25 citations

Persistent currents in the one-dimensional mesoscopic Hubbard ring

Bo-Bo Wei, Shi-Jian Gu, Hai‐Qing Lin

In this paper, we study persistent charge and spin currents in the ground state of the one-dimensional mesoscopic Hubbard ring with repulsive interaction based on its Bethe-ansatz solution. We find that the persistent charge current is suppressed by the on-site Coulomb interaction more significantly at half-filling than away from half-filling. As the system size increases the charge current decays exponentially as I ∼ L −1 e − L /ξ in the half-filling case and decays in a power law away from the half-filling case. We also find that the persistent spin current is suppressed by the on-site Coulomb interaction, and it decays algebraically as the system size increases both at half-filling and away from half-filling.

Journal of Physics Condensed Matter•Sep 1, 2008•13 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 a one-dimensional disordered ring in the Luttinger model

Jia‐Lin Zhu, Xi Chen, Yoshiyuki Kawazoe

The Luttinger model is extended to include disorder effects in ring geometry. The persistent current in a mesoscopic ring is evaluated using the concept of topological excitations and path integrals in a multiply connected system. It is found that the repulsive interaction counteracts the effect of disorder and enhances the amplitude of the current. The interplay between interaction and disorder is manifested clearly in the model calculation.

Physical review. B, Condensed matter•Jun 15, 1997•2 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 Coulomb Interactions on The Amplitude Of Persistent Currents In One Dimensional Disordered Mesoscopic Metallic Rings

Robinson O. Okanigbuan, Kingsley N. Onaiwu, S. Ehika

Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb interaction is observed to enhance the persistent current. Furthermore, in the half-filled case, there is a transition from metal to insulator as U is increased significantly. In addition, shifting away from half-filling, the system is observed to remain in the metallic state irrespective of the value of the Coulomb repulsion (U). The observations are quite in agreement with the results from other techniques.

arXiv:2107.02078•Jul 5, 2021•0 citations
We consider a one-dimensional Hubbard model in the presence of disorder. We compute the charge stiffness for a mesoscopic ring as a function of the size L, which is a measure of the persistent currents. We find that for finite disorder the persistent currents of the system with repulsive interactions are larger than those of the system with attractive interactions. This counterintuitive result is due to the fact that local-density fluctuations are reduced in the presence of repulsive interactions.
We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.
In this paper, we study persistent charge and spin currents in the ground state of the one-dimensional mesoscopic Hubbard ring with repulsive interaction based on its Bethe-ansatz solution. We find that the persistent charge current is suppressed by the on-site Coulomb interaction more significantly at half-filling than away from half-filling. As the system size increases the charge current decays exponentially as I ∼ L −1 e − L /ξ in the half-filling case and decays in a power law away from the half-filling case. We also find that the persistent spin current is suppressed by the on-site Coulomb interaction, and it decays algebraically as the system size increases both at half-filling and away from half-filling.
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.
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.
Persistent current is a small but perpetual electric current that flows in metallic rings in the absence of any applied source. We compute the persistent currents of one-dimensional disordered metallic rings of interacting electrons in the presence of impurity on lattices up to 8-sites at half-filling and also away from half-filling using the Lanczos algorithm. For the case of half-filling, we observe that both interaction and disorder suppress the amplitude of the persistent currents by localizing the electrons. However, in the presence of disorder and away from half-filling, the Coulomb interaction is observed to enhance the persistent current. Furthermore, in the half-filled case, there is a transition from metal to insulator as U is increased significantly. In addition, shifting away from half-filling, the system is observed to remain in the metallic state irrespective of the value of the Coulomb repulsion (U). The observations are quite in agreement with the results from other techniques.