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

Search for superconductivity in an extended Hubbard model

S. N. Coppersmith

Published May 1, 1989• 8 citations
Publisher

Abstract

Extensions of the Gutzwiller variational method are used to study whether substantial nearest-neighbor repulsion between holes on a copper-oxygen lattice in two dimensions leads to simple s-wave superconductivity. It is found that the simplest one-parameter s-wave superconducting wave functions do not lower the energy with respect to the normal state.

DOI
10.1103/physrevb.39.9671

Related papers

Superconducting states of an extended Hubbard model

S. N. Coppersmith

The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.

Physical review. B, Condensed matter•Aug 1, 1990•15 citations

Normal and antiferromagnetic states of an extended Hubbard model

S. N. Coppersmith

Variational Monte Carlo calculations using extensions of the Gutzwiller variational wave function are used to study the phase diagram of an extended Hubbard model on a copper-oxygen lattice in two dimensions. Antiferromagnetism appears to occur at half-filling only when the oxygen p levels and copper d levels have substantially different energies. It is also found that strong nearest-neighbor repulsions can enhance the tendency for local-moment antiferromagnetism. The dependence of the variational parameters on the Hamiltonian parameters, particularly nearest-neighbor repulsions, is examined. The implications for models of high-temperature superconductivity are discussed.

Physical review. B, Condensed matter•May 1, 1990•14 citations

Superconductivity in the two-dimensional Hubbard model: Gutzwiller wave function solution

Jan Kaczmarczyk, Józef Spałek, Tobias Schickling +1 more

A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes $t$ (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters ($U$, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.

arXiv:1210.6249•Physical Review B•Sep 16, 2013•64 citations

Superconductivity in the repulsive Hubbard model

D. Baeriswyl

The two-dimensional repulsive Hubbard model has been investigated by a variety of methods, from small to large U. Superconductivity with d-wave symmetry is consistently found close to half filling. After a brief review of the various methods a variational many-electron state is discussed in more detail. This trial state is a natural extension of the Gutzwiller ansatz and provides a substantial improvement thereof.

arXiv:1010.6137•Oct 29, 2010•0 citations

Variational Monte Carlo Indications ofd-Wave Superconductivity in the Two-Dimensional Hubbard Model

Takeshi Nakanishi, Yamaji K., Takashi Yanagisawa

The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.

Journal of the Physical Society of Japan•Feb 15, 1997•65 citations

Electronic model for superconductivity

Fabian H. L. Eßler, V. E. Korepin, Kareljan Schoutens

We consider a model of strongly correlated electrons that exhibits superconductivity. It differs from the Hubbard model by nearest-neighbor interactions. We find the ground-state wave function (in one, two, or three dimensions) and show it to be superconducting for attractive and moderately repulsive on-site interaction.

Physical Review Letters•Jan 4, 1993•138 citations
Extensions of the Gutzwiller variational method are used to study whether substantial nearest-neighbor repulsion between holes on a copper-oxygen lattice in two dimensions leads to simple s-wave superconductivity. It is found that the simplest one-parameter s-wave superconducting wave functions do not lower the energy with respect to the normal state.
The variational Monte Carlo method is used to study possible superconducting states of a two-dimensional extended Hubbard model on a copper-oxygen lattice. It is found that d-wave and extended s-wave superconducting variational wave functions can have lower energy than the corresponding normal state for different parameter regions, while simple s-wave superconductivity is never favored. Increasing the nearest-neighbor repulsion and decreasing the copper-oxygen level separation can promote extended s-wave superconductivity and inhibit d-wave superconductivity.
Variational Monte Carlo calculations using extensions of the Gutzwiller variational wave function are used to study the phase diagram of an extended Hubbard model on a copper-oxygen lattice in two dimensions. Antiferromagnetism appears to occur at half-filling only when the oxygen p levels and copper d levels have substantially different energies. It is also found that strong nearest-neighbor repulsions can enhance the tendency for local-moment antiferromagnetism. The dependence of the variational parameters on the Hamiltonian parameters, particularly nearest-neighbor repulsions, is examined. The implications for models of high-temperature superconductivity are discussed.
A systematic diagrammatic expansion for Gutzwiller-wave functions (DE-GWF) is formulated and used for the description of superconducting (SC) ground state in the two-dimensional Hubbard model with electron-transfer amplitudes ttt (and ${t}^{\ensuremath{'}}$) between nearest (and next-nearest) neighbors. The method is numerically very efficient and allows for a detailed analysis of the phase diagram as a function of all relevant parameters (UUU, $\ensuremath{\delta}$, ${t}^{\ensuremath{'}}$) and a determination of the kinetic-energy driven pairing region. SC states appear only for substantial interactions, $U/t\ensuremath{\gtrsim}3$, and for not too large hole doping, $\ensuremath{\delta}\ensuremath{\lesssim}0.32$ for ${t}^{\ensuremath{'}}=0.25t$; this upper critical doping value agrees well with experiment for the cuprate high-temperature superconductors. We also obtain other important features of the SC state: (i) the SC gap at the Fermi surface resembles ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave only around the optimal doping and the corrections to this state are shown to arise from the longer range of the pairing; (ii) the nodal Fermi velocity is almost constant as a function of doping and agrees quantitatively with the experimental results; (iii) the SC transition is driven by the kinetic-energy lowering for low doping and strong interactions.
The possibility of superconductivity in the ground state of the two-dimensional Hubbard model was investigated by means of the variational Monte Carlo method. With slight hole doping on the 6 ×6 and 10 ×10 lattices, a clear minimum was obtained on the curve of the total energy versus the amplitude of the d -wave gap function for large on-site Coulomb energies. Superconducting pair correlations were observed to be well developed. The-next-nearest-neighbor transfer was found to appreciably affect the minimum depth.