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

Journal of Physics Condensed Matter

Persistent currents in the one-dimensional mesoscopic Hubbard ring

Bo-Bo Wei, Shi-Jian Gu, Hai‐Qing Lin

Published Sep 1, 2008• 13 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/20/39/395209

Related papers

Persistent currents and spin-charge separation in a one-dimensional Hubbard ring with side sites

W. Z. Wang

The persistent current and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion $U$ increases, the sign of the current may oscillate depending on the total number of electrons ${N}_{e}$ and the hopping $t$ between the ring site and the side site. For small hopping $t$, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate $U$ can strongly enhance the persistent current while the hopping $t$ always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large $U$ and small $t$ case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.

Physical Review B•Feb 6, 2007•3 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

Large system asymptotics of persistent currents in mesoscopic quantum rings

Andrej Gendiar, Roman Krčmár, Michael Weyrauch

We consider a one-dimensional mesoscopic quantum ring filled with spinless electrons and threaded by a magnetic flux, which carries a persistent current at zero temperature. The interplay of Coulomb interactions and a single on-site impurity yields a nontrivial dependence of the persistent current on the size of the ring. We determine numerically the asymptotic power law for systems up to $32\text{ }000$ sites for various impurity strengths and compare with predictions from Bethe ansatz solutions combined with bosonization. The numerical results are obtained using an improved functional renormalization-group (fRG) method. We apply the density-matrix renormalization-group (DMRG) and exact diagonalization methods to benchmark the fRG calculations. We use DMRG to study the persistent current at low electron concentrations in order to extend the validity of our results to quasicontinuous systems. We briefly comment on the quality of calculated fRG ground-state energies by comparison with exact DMRG data.

arXiv:0902.4385•Physical Review B•May 26, 2009•7 citations

Persistent current and Drude weight in mesoscopic rings

F. Carvalho Dias, Iveta R. Pimentel, Malte Henkel

We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a density matrix renormalization group (DMRG) algorithm for complex fields. Both the Luttinger liquid (LL) and the charge density wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-$1∕2$ $XXZ$ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay with the system size, as the system crosses from the LL to the CDW phase with increasing interaction $U$. We also find that in the interacting system, the persistent current is invariant under the impurity transformation $\ensuremath{\rho}\ensuremath{\rightarrow}1∕\ensuremath{\rho}$, for large system sizes, where $\ensuremath{\rho}$ is the defect strength. The persistent current exhibits a decay that is in agreement with the behavior obtained for the Drude weight. We find that in the LL phase the Drude weight decreases algebraically with the number of lattice sites $N$, due to the interplay of the electron interaction with the impurity, while in the CDW phase, it decreases exponentially, defining a localization length which decreases with increasing interaction and impurity strength. Our results show that the impurity and the interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ in both phases.

arXiv:cond-mat/0506654•Physical Review B•Feb 14, 2006•22 citations

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

Thierry Giamarchi, B. Sriram Shastry

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.

arXiv:cond-mat/9411063•Physical review. B, Condensed matter•Apr 15, 1995•146 citations

Persistent currents in one-dimensional disordered rings of interacting electrons

G. Bouzerar, Didier Poilblanc, Gilles Montambaux

We calculate the persistent current of one-dimensional rings of spinless fermions with short-range interactions on a lattice with up to 20 sites, and in the presence of disorder, for various band fillings. We find that both disorder and interactions always decrease the persistent current by localizing the electrons. Away from half-filling, the interaction has a much stronger influence in the presence of disorder than in the pure case.

arXiv:cond-mat/9310007•Physical review. B, Condensed matter•Mar 15, 1994•155 citations
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 and spin-charge separation are studied in a one-dimensional (1D) Hubbard ring with side sites connected to the even sites of the ring. At half filling, the persistent current is always paramagnetic and has a period of flux quantum. Away from half filling, as the onsite repulsion UUU increases, the sign of the current may oscillate depending on the total number of electrons Ne{N}_{e}Ne​ and the hopping ttt between the ring site and the side site. For small hopping ttt, the number of electrons ${N}_{e}^{\ensuremath{'}}$ in the ring sites plays an important role in determining the sign of the current. In contrast to the 1D Hubbard model, a weak or a moderate UUU can strongly enhance the persistent current while the hopping ttt always suppresses the current. The study on the transmittance of the ring with two connected leads indicates that in the large UUU and small ttt case, the transmittance varies with a period $1∕{N}_{e}^{\ensuremath{'}}$ of a flux quantum, demonstrating a spin-charge separation in this system.
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.
We consider a one-dimensional mesoscopic quantum ring filled with spinless electrons and threaded by a magnetic flux, which carries a persistent current at zero temperature. The interplay of Coulomb interactions and a single on-site impurity yields a nontrivial dependence of the persistent current on the size of the ring. We determine numerically the asymptotic power law for systems up to 32 00032\text{ }00032 000 sites for various impurity strengths and compare with predictions from Bethe ansatz solutions combined with bosonization. The numerical results are obtained using an improved functional renormalization-group (fRG) method. We apply the density-matrix renormalization-group (DMRG) and exact diagonalization methods to benchmark the fRG calculations. We use DMRG to study the persistent current at low electron concentrations in order to extend the validity of our results to quasicontinuous systems. We briefly comment on the quality of calculated fRG ground-state energies by comparison with exact DMRG data.
We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a density matrix renormalization group (DMRG) algorithm for complex fields. Both the Luttinger liquid (LL) and the charge density wave (CDW) phases of the system are considered. Under a Jordan-Wigner transformation, the system is equivalent to a spin-1∕21∕21∕2 XXZXXZXXZ chain with a weakened exchange coupling. We find that the persistent current changes from an algebraic to an exponential decay with the system size, as the system crosses from the LL to the CDW phase with increasing interaction UUU. We also find that in the interacting system, the persistent current is invariant under the impurity transformation $\ensuremath{\rho}\ensuremath{\rightarrow}1∕\ensuremath{\rho}$, for large system sizes, where $\ensuremath{\rho}$ is the defect strength. The persistent current exhibits a decay that is in agreement with the behavior obtained for the Drude weight. We find that in the LL phase the Drude weight decreases algebraically with the number of lattice sites NNN, due to the interplay of the electron interaction with the impurity, while in the CDW phase, it decreases exponentially, defining a localization length which decreases with increasing interaction and impurity strength. Our results show that the impurity and the interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ in both phases.
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.