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

Parity-locking effect in a strongly-correlated ring

C. A. Stafford, D. F. Wang

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder. The free energy F(φ) of a metallic ring threaded by an Aharonov-Bohm flux (¯hc/e)φ is a periodic function of φ, with period 2π [1]. The system is said to be diamagnetic if F is minimal for φ = 0, and paramagnetic if F is minimal for φ = π (1/2 flux quantum). A purely one-dimensional (1D) ring with N spinless electrons is diamagnetic if N is even and paramagnetic if N is odd, independent

Related papers

Interaction-induced enhancement and oscillations of the persistent current

Charles Allen Stafford, D. F. Wang

The persistent current $I$ in integrable models of multichannel rings with both short- and long-ranged interactions is investigated. $I$ is found to oscillate in sign and increase in magnitude with increasing interaction strength due to interaction-induced correlations in the currents contributed by different channels. For sufficiently strong interactions, the contributions of all channels are found to add constructively, leading to a giant enhancement of $I.$ Numerical results confirm that this parity-locking effect is robust with respect to intersubband scattering.

arXiv:cond-mat/9701026•Physical review. B, Condensed matter•Aug 15, 1997•6 citations

Finite-width altermagnetic quantum rings: angular-channel hybridization and Aharonov--Bohm physics

Edilberto O. Silva

We study a finite-width two-dimensional quantum ring with a quadratic $d$-wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes $m$ and $m\pm2$ angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for $N_e=1400$ and $1800$ establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.

cond-mat.mes-hallCross-listedarXiv:2610.30536•Oct 23, 2026

Parity effects in a Luttinger liquid: Diamagnetic and paramagnetic ground states

Daniel Loss

The concept of a Luttinger liquid in 1D is extended to include twisted boundary conditions on a ring and mesoscopic parity effects due to evenness and oddness of the particle number ${\mathit{N}}_{0}$. Using Haldane's notion of topological excitations, a proof of Leggett's conjecture is presented, stating that the ground state of interacting 1D quantum systems is diamagnetic or paramagnetic depending on the parity of ${\mathit{N}}_{0}$. The persistent currents produced by an Aharonov-Bohm flux are calculated and shown to have period and amplitude that are in agreement with recent experiments.

Physical Review Letters•Jul 13, 1992•204 citations

The fractional Aharonov - Bohm effect in mesoscopic rings

V Ferrari, G. Chiappe

We study the effects of correlations on a one-dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the Hubbard model and the t - and t - - models. We focus on the dilute limit. Our results suggest the possibility that the persistent current has an anomalous periodicity , where p is an integer in the range ( is the number of particles in the ring and is the flux quantum). We find that this result depends neither on disorder nor on the detailed form of the interaction, while there is still on-site infinite repulsion.

arXiv:cond-mat/9603191•Journal of Physics Condensed Matter•Oct 28, 1996•6 citations

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 currents in multichannel interacting systems

G. Bouzerar, Didier Poilblanc

Persistent currents in disordered multichannel mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock treatments of two-dimensional tori and cylinders of spinless interacting fermions. The validity of the Hartree-Fock approximation is controlled by a direct comparison with the exact results on small 4\ifmmode\times\else\texttimes\fi{}4 clusters. The existence of a crossover value for the disorder parameter ${\mathit{W}}_{\mathit{c}}$ (depending on the electronic density and the system size) separating two different regimes is established. Decomposing the current I(\ensuremath{\varphi}) in terms of its fundamental harmonics, we find that, while the first harmonic is always enhanced by the interaction, the second harmonic is enhanced for W${\mathit{W}}_{\mathit{c}}$ and strongly suppressed otherwise. This effect is stronger as we increase the disorder.

arXiv:cond-mat/9412086•Physical review. B, Condensed matter•Oct 15, 1995•27 citations
Orbital magnetism in an integrable model of a multichannel ring with long-ranged electron-electron interactions is investigated. In a noninteracting multichannel system, the response to an external magnetic flux is the sum of many diamagnetic and paramagnetic contributions, but we find that for sufficiently strong correlations, the contributions of all channels add constructively, leading to a parity (diamagnetic or paramagnetic) which depends only on the total number of electrons. Numerical results confirm that this parity-locking effect is robust with respect to subband mixing due to disorder. The free energy F(φ) of a metallic ring threaded by an Aharonov-Bohm flux (¯hc/e)φ is a periodic function of φ, with period 2π [1]. The system is said to be diamagnetic if F is minimal for φ = 0, and paramagnetic if F is minimal for φ = π (1/2 flux quantum). A purely one-dimensional (1D) ring with N spinless electrons is diamagnetic if N is even and paramagnetic if N is odd, independent
The persistent current III in integrable models of multichannel rings with both short- and long-ranged interactions is investigated. III is found to oscillate in sign and increase in magnitude with increasing interaction strength due to interaction-induced correlations in the currents contributed by different channels. For sufficiently strong interactions, the contributions of all channels are found to add constructively, leading to a giant enhancement of I.I.I. Numerical results confirm that this parity-locking effect is robust with respect to intersubband scattering.
We study a finite-width two-dimensional quantum ring with a quadratic ddd-wave altermagnetic term, Tan--Inkson confinement, a perpendicular magnetic field, and independently tunable Aharonov--Bohm (AB) flux. The altermagnetic interaction mixes mmm and m±2m\pm2m±2 angular channels while preserving their parity. Circular symmetry renders the crystal orientation spectrally irrelevant and makes the two spin blocks exactly isospectral. The resulting same-parity anticrossings are resolved at low filling, and multichannel mixing is found near the Fermi level of highly occupied rings. Independent converged calculations for Ne=1400N_e=1400Ne​=1400 and 180018001800 establish the reconstructed Fermi edge and magnetic response in a finite field window and the persistent current over a full AB flux period. The analytic conventional reference separates radial-subband depopulation (dHvA-type cycles) from finer finite-ring shell oscillations; we do not assign a global Fourier spectrum to unverified altermagnetic field scans. The few-electron thermal response is obtained from an exact fixed-particle-number canonical partition function, avoiding finite-system errors of a fixed-mean-number approximation. The circular model supports an equilibrium charge current but no persistent spin current.
The concept of a Luttinger liquid in 1D is extended to include twisted boundary conditions on a ring and mesoscopic parity effects due to evenness and oddness of the particle number N0{\mathit{N}}_{0}N0​. Using Haldane's notion of topological excitations, a proof of Leggett's conjecture is presented, stating that the ground state of interacting 1D quantum systems is diamagnetic or paramagnetic depending on the parity of N0{\mathit{N}}_{0}N0​. The persistent currents produced by an Aharonov-Bohm flux are calculated and shown to have period and amplitude that are in agreement with recent experiments.
We study the effects of correlations on a one-dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the Hubbard model and the t - and t - - models. We focus on the dilute limit. Our results suggest the possibility that the persistent current has an anomalous periodicity , where p is an integer in the range ( is the number of particles in the ring and is the flux quantum). We find that this result depends neither on disorder nor on the detailed form of the interaction, while there is still on-site infinite repulsion.
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.
Persistent currents in disordered multichannel mesoscopic rings threaded by a magnetic flux are calculated using exact diagonalizations and self-consistent Hartree-Fock treatments of two-dimensional tori and cylinders of spinless interacting fermions. The validity of the Hartree-Fock approximation is controlled by a direct comparison with the exact results on small 4\ifmmode\times\else\texttimes\fi{}4 clusters. The existence of a crossover value for the disorder parameter Wc{\mathit{W}}_{\mathit{c}}Wc​ (depending on the electronic density and the system size) separating two different regimes is established. Decomposing the current I(\ensuremath{\varphi}) in terms of its fundamental harmonics, we find that, while the first harmonic is always enhanced by the interaction, the second harmonic is enhanced for WWc{\mathit{W}}_{\mathit{c}}Wc​ and strongly suppressed otherwise. This effect is stronger as we increase the disorder.