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

Physical review. B, Condensed matter

Flux quantization in rings for Hubbard (attractive and repulsive) and t - J -like Hamiltonians

Alessandro Ferretti, I. O. Kulik, Alessandro Lami

Published Mar 1, 1992• 18 citations
Publisher

Abstract

The ground-state energy of rings with 10 or 16 sites and 2 or 4 fermions (holes or electrons) is computed as a function of the flux \ensuremath{\Phi} created by a vector potential constant along the ring (Aharonov-Bohm setup) for three different model Hamiltonians: the attractive (U0) and repulsive (U>0) Hubbard and a t-J-like Hamiltonian. In all cases the flux is found to be quantized in units hc/2e, showing that the charge carriers are pairs. The possible role of phonon fluctuations in discriminating among the different models is also investigated.

DOI
10.1103/physrevb.45.5486

Related papers

Comment on ‘‘Flux quantization in rings for Hubbard (attractive and repulsive) andt-J-like Hamiltonians’’

Liang Chen, Changjiang Mei, A.–M. S. Tremblay

It is shown for three models with strong correlations that the value of the total spin of the ground state of finite-size rings with two fermions (holes or electrons) can change as a function of magnetic flux \ensuremath{\Phi}. It is concluded that the magnetic flux periodicity may be used as a test of binding only if one also checks for changes in spin quantum numbers.

Physical review. B, Condensed matter•Jun 1, 1993•2 citations

Flux quantization in the two-dimensional repulsive and attractive Hubbard models

Fakher F. Assaad, Werner R. Hanke, Douglas J. Scalapino

In order to provide a numerical criterion for superconductivity, the ground state energy ${\mathit{E}}_{0}$(\ensuremath{\Phi}) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. From the functional form of ${\mathit{E}}_{0}$(\ensuremath{\Phi}), superconducting ground states may be identified without prior knowledge of the pairing symmetry. ${\mathit{E}}_{0}$(\ensuremath{\Phi}) is calculated with Monte Carlo methods. For the attractive Hubbard model, our results confirm the existence of a superconducting ground state. In contrast, our results show that the quarter-filled repulsive Hubbard model is not superconducting and that a Hartree-Fock paramagnetic approximation fits the data very well.

Physical Review Letters•Sep 20, 1993•35 citations

Flux-quantization in one-dimensional copper-oxide models

Chandra Mohan Varma, Asle Sudbø

A calculation of the ground state energy E0(Φ) as a function of flux Φ in a one-dimensional `copper-oxide model' on rings of finite circumference L, including on-site interactions, and a nearest neighbor interaction V, is presented. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux-quantization with charge 2e. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.

Journal de Physique I•Feb 1, 1993•2 citations

Exact solution of the one-dimensional Hubbard model in a magnetic field

Gang Su, Bao‐Heng Zhao, Mo‐Lin Ge

By means of the Bethe-ansatz method, the one-dimensional Hubbard model with repulsive on-site coupling in an external magnetic field is solved exactly. It is found that the energy of the ground state depends on the magnetic flux \ensuremath{\varphi} through the ring formed by a periodic lattice chain, and the lowest-energy state corresponds to \ensuremath{\varphi}=n(hc/2e), with n an integer and -e the electron charge. The calculations illustrate that the strongly correlated Hubbard ring with periodic boundary conditions in its ground state is a superconducting ring. It can also be shown that the system possesses an internal SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry.

Physical review. B, Condensed matter•Dec 1, 1992•4 citations

Repulsion-sustained supercurrent and flux quantization in rings of symmetric Hubbard clusters

Agnese Callegari, Michele Cini, Enrico Perfetto +1 more

We test the response to a threading magnetic field of rings of five-site ${C}_{4v}$-symmetric repulsive Hubbard clusters connected by weak intercell links; each five-site unit has the topology of a ${\mathrm{CuO}}_{4}$ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with eight particles, we take advantage of an exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find a superconducting flux quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with $W=0$ pairing theory.

arXiv:cond-mat/0309036•Physical review. B, Condensed matter•Oct 16, 2003•3 citations

Flux quantization and diamagnetic currents in strongly correlated systems

A. Ferretti, I. O. Kulik, A. Lami

Within the basic assumption that oxygen orbitals may play a fundamental role in the superconductive properties of Cu-O high-${\mathit{T}}_{\mathit{c}}$ materials, exact calculations of the ground-state energy and thermodynamic properties of strongly interacting fermions in small oxygen rings have been performed. Persistent currents (mesoscopic effect) and supercurrents have been computed for several microscopic models including repulsive and attractive Hubbard and the occupation-dependent hopping Hamiltonians. It is shown that for a given range of parameters the latter model exhibits features reminiscent of superconductivity: a maximum in the temperature dependence of the specific heat, whose position correlates with the temperature at which the superelectron concentration vanishes and exact hc/2e-periodic dependence of the free energy as a function of magnetic flux.

Physical review. B, Condensed matter•May 1, 1993•13 citations
The ground-state energy of rings with 10 or 16 sites and 2 or 4 fermions (holes or electrons) is computed as a function of the flux \ensuremath{\Phi} created by a vector potential constant along the ring (Aharonov-Bohm setup) for three different model Hamiltonians: the attractive (U0) and repulsive (U>0) Hubbard and a t-J-like Hamiltonian. In all cases the flux is found to be quantized in units hc/2e, showing that the charge carriers are pairs. The possible role of phonon fluctuations in discriminating among the different models is also investigated.
In order to provide a numerical criterion for superconductivity, the ground state energy E0{\mathit{E}}_{0}E0​(\ensuremath{\Phi}) is calculated for the attractive and repulsive Hubbard models on a cylinder geometry threaded by a flux \ensuremath{\Phi}. From the functional form of E0{\mathit{E}}_{0}E0​(\ensuremath{\Phi}), superconducting ground states may be identified without prior knowledge of the pairing symmetry. E0{\mathit{E}}_{0}E0​(\ensuremath{\Phi}) is calculated with Monte Carlo methods. For the attractive Hubbard model, our results confirm the existence of a superconducting ground state. In contrast, our results show that the quarter-filled repulsive Hubbard model is not superconducting and that a Hartree-Fock paramagnetic approximation fits the data very well.
A calculation of the ground state energy E0(Φ) as a function of flux Φ in a one-dimensional `copper-oxide model' on rings of finite circumference L, including on-site interactions, and a nearest neighbor interaction V, is presented. For V of the order of the charge-transfer gap or larger, the model extrapolated to large L exhibits flux-quantization with charge 2e. The extrapolated superfluid stiffness appears, however, finite only for not too large V. These results suggest a superconductive state at V of order the charge-transfer gap of the model, but a paired and phase-separated state at larger V.
By means of the Bethe-ansatz method, the one-dimensional Hubbard model with repulsive on-site coupling in an external magnetic field is solved exactly. It is found that the energy of the ground state depends on the magnetic flux \ensuremath{\varphi} through the ring formed by a periodic lattice chain, and the lowest-energy state corresponds to \ensuremath{\varphi}=n(hc/2e), with n an integer and -e the electron charge. The calculations illustrate that the strongly correlated Hubbard ring with periodic boundary conditions in its ground state is a superconducting ring. It can also be shown that the system possesses an internal SU(2)\ifmmode\times\else\texttimes\fi{}SU(2) symmetry.
We test the response to a threading magnetic field of rings of five-site C4v{C}_{4v}C4v​-symmetric repulsive Hubbard clusters connected by weak intercell links; each five-site unit has the topology of a CuO4{\mathrm{CuO}}_{4}CuO4​ cluster and a repulsive interaction is included on every site. In a numerical study of the three-unit ring with eight particles, we take advantage of an exact-diagonalization technique which can be generally applied to many-fermion problems. For O-O hopping we find a superconducting flux quantization (SFQ), but for purely Cu-Cu links bound pair propagation is hindered by symmetry. The results agree with W=0W=0W=0 pairing theory.
Within the basic assumption that oxygen orbitals may play a fundamental role in the superconductive properties of Cu-O high-Tc{\mathit{T}}_{\mathit{c}}Tc​ materials, exact calculations of the ground-state energy and thermodynamic properties of strongly interacting fermions in small oxygen rings have been performed. Persistent currents (mesoscopic effect) and supercurrents have been computed for several microscopic models including repulsive and attractive Hubbard and the occupation-dependent hopping Hamiltonians. It is shown that for a given range of parameters the latter model exhibits features reminiscent of superconductivity: a maximum in the temperature dependence of the specific heat, whose position correlates with the temperature at which the superelectron concentration vanishes and exact hc/2e-periodic dependence of the free energy as a function of magnetic flux.