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/9411068 · Physical review. B, Condensed matter

Interplay between electron-electron interactions and impurities in one-dimensional rings

弘之 森

Published May 15, 1995• 11 citations
arXivHTMLPDF

Abstract

The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.

DOI
10.1103/physrevb.51.12943

Related papers

Correlation Effects in One-dimensional Electron Systems

P. Sandström

Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.

•Jan 1, 1998•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 current and Drude weight of one-dimensional interacting fermions on imperfect ring from current lattice density functional theory

Akinlolu Akande, Stefano Sanvito

We perform a numerical study of interacting one-dimensional Hubbard rings with a single impurity potential and pierced by a magnetic flux. Our calculations are carried out at the level of current lattice density functional theory (CLDFT) for the Hubbard model and compared to known results obtained in the thermodynamical limit from the Bethe ansatz. In particular, we investigate the effects of disorder and Coulomb interaction on the persistent current (PC) and the Drude weight. It is found that CLDFT is able to accurately describe qualitative and quantitative features of these ground state properties in the presence of disorder and electronic interaction. When the impurity potential is switched off, the CLDFT approach describes well the velocity of the Luttinger liquid excitations as a function of both interaction strength and electron filling. Then, when the impurity scattering potential is finite, we find the PC to vanish as [Formula: see text] for large L and independent on the strength of the scattering potential, in good agreement with Luttinger liquid theory.

Journal of Physics Condensed Matter•Sep 8, 2016•1 citation

Persistent current in a two-chain Hubbard model with impurities

弘之 森

The interplay between impurities and interactions is studied in the gapless phase in a two-chain Hubbard model in order to see how the screening of impurity potentials due to repulsive interactions in a single-chain model will be changed by increasing the number of channels. Renormalization-group calculations show that charge stiffness, and hence persistent current, of the two-chain model are less enhanced by interactions than in the single-chain case.

arXiv:cond-mat/9804265•Physical review. B, Condensed matter•Aug 15, 1998•1 citation

Persistent currents in one-dimensional systems of strongly correlated electrons (review)

Andrei A. Zvyagin, Ilya V. Krive

Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.

Low Temperature Physics•Jul 1, 1995•11 citations

Persistent current for a Luttinger liquid

D. Schmeltzer

We compute the current for a Luttinger ring treated by a magnetic flux at T=0 and T\ensuremath{\ne}0. We find that the current depends on the stiffness. The current is reduced with increase of the interaction strength and size of the ring. A scaling law, which relates the current in the presence of interaction to the noninteracting case, is obtained.

Physical review. B, Condensed matter•Mar 15, 1993•12 citations
The persistent current and charge stiffness of a one-dimensional Luttinger liquid on a ring threaded by a magnetic flux are calculated by Monte Carlo simulation. By changing the random impurity potential strength and the electron-electron interaction, we see a crossover behavior between weak- and strong-impurity limits. For weak-impurity potentials, interactions enhance impurity effects, that is, interactions decrease the current and the stiffness. On the other hand, interactions tend to screen impurities when the impurity potential is strong. Temperature dependence of the persistent current and the charge stiffness shows a peak at a characteristic temperature, consistent with a recent single-impurity study.
Theoretical studies suggest that an interacting one-dimensional electron system does not behave as a Fermi liquid. Instead, it is predicted to form a Luttinger liquid characterized e.g. by the absence of fermionic quasiparticles and interaction-dependent power-laws for transport quantities. So far, however, only a limited number of experiments have provided evidence for Luttinger liquid behavior. In this thesis we consider alternative methods to detect electronic correlations in one-dimensional electron systems based on our calculations of persistent currents and quantization of charge in ballistic single channel rings. The persistent current in an isolated impurity-free Luttinger liquid ring is found to be the same as for a system of non-interacting electrons. In contrast, a Luttinger liquid behavior is revealed if the ring is weakly connected to an electron reservoir and capacitively coupled to a gate electrode. The persistent current and the average charge in the ring are shown to change in a stepwise manner with the gate voltage at low temperatures. Both the step positions and the crossover temperatures are determined by the Luttinger liquid correlation parameter .alpha.(.alpha.c) which therefore can be measured. When a potential barrier is incorporated into the ring, the presence of strong interactions between electrons leads to a suppression of the persistent current and a change in its temperature dependence. A sharp maximum of the current is predicted to occur as a function of temperature. When two barriers are introduced into the ring, the possibility of resonant tunneling for the persistent current opens up. Two kinds of resonant behavior are discovered in the closed geometry: a current independent of the barrier transparency and a current analogous to the one with a single potential barrier. The persistent current in a ring containing a gas of fractionally charged excitations obeying fractional exclusion statistics is also studied. At finite temperatures, anomalous oscillations of the current are predicted as a manifestation of the statistics of the quasiparticles.
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 perform a numerical study of interacting one-dimensional Hubbard rings with a single impurity potential and pierced by a magnetic flux. Our calculations are carried out at the level of current lattice density functional theory (CLDFT) for the Hubbard model and compared to known results obtained in the thermodynamical limit from the Bethe ansatz. In particular, we investigate the effects of disorder and Coulomb interaction on the persistent current (PC) and the Drude weight. It is found that CLDFT is able to accurately describe qualitative and quantitative features of these ground state properties in the presence of disorder and electronic interaction. When the impurity potential is switched off, the CLDFT approach describes well the velocity of the Luttinger liquid excitations as a function of both interaction strength and electron filling. Then, when the impurity scattering potential is finite, we find the PC to vanish as [Formula: see text] for large L and independent on the strength of the scattering potential, in good agreement with Luttinger liquid theory.
Charge persistent currents in single-channel ballistic rings are investigated in various models of strongly correlated electrons (Wigner crystal, Luttinger liquid, Hubbard model, t–J model, and the fermion representation of the Heisenberg–Ising model). The primary objective of the survey is to compare the properties of Aharonov–Bohm oscillations for weakly and strongly correlated electrons and to formulate a set of persistent current characteristics that will unambiguously support the anomalous (departing from a Fermi liquid) behavior of one-dimensional electron systems. For this purpose the onset of the parity effect (dependence of the system response on whether the number of particles in the ring is odd or even) and various properties of the persistent current are analyzed in detail for model spinless fermions and real electrons. The influence of solitary impurities on the value and temperature dependence of the amplitude of the Aharanov–Bohm oscillations is also investigated. It is shown that the formation of a Wigner crystal (which is possible for weakly shielded Coulomb interaction) leads to a very pronounced anomalous (nonmonotonic) temperature dependence of the current in a nonideal ring. The properties of the charge current near the Mott metal–insulator transition are altered to the greatest degree by local types of electron–electron interaction.