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

Enhanced pairing in the repulsive Hubbard model with next-nearest-neighbor hopping

Raimundo R. dos Santos

Published Apr 1, 1989• 28 citations
Publisher

Abstract

We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping ${t}_{2}$ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with ${t}_{2}$=0. We discuss the connection of this model to ${\mathrm{CuO}}_{2}$ planes in the oxide superconductors and the possible implication of our results for these materials.

DOI
10.1103/physrevb.39.7259

Related papers

Pairing in the two-dimensional Hubbard model: A Monte Carlo study

J. E. Hirsch, H. Q. Lin

We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-${T}_{c}$ superconductivity in oxides are discussed.

Physical review. B, Condensed matter•Apr 1, 1988•95 citations

Two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping

H. Q. Lin, J. E. Hirsch

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (${t}_{2}$) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if ${t}_{2}$\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.

Physical review. B, Condensed matter•Mar 1, 1987•185 citations

Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping

Alain Veilleux, A.-M. Daré, Liang Chen +2 more

A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.

arXiv:cond-mat/9507045•Physical review. B, Condensed matter•Dec 1, 1995•40 citations

Langevin Simulation of the Two-Dimensional Hubbard Model

Kazuo Saitoh, Satoshi Takada

The two-dimensional (2-D) Hubbard model with nearest-neighbor and next-nearest-neighbor (n.n.n.) hopping are studied using the Langevin method. Results of the staggered magnetic susceptibility and the pairing susceptibilities are shown. It is found that the effect of n.n.n. hopping destroys the antiferromagnetic correlation and assists the tendency of pairing. The possibility of superconductivity in the Hubbard model in the presence of n.n.n. hopping is discussed.

Journal of the Physical Society of Japan•Mar 15, 1989•6 citations

Second-neighbor hopping in the attractive Hubbard model

Raimundo R. dos Santos

We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (${\mathit{t}}_{2}$) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert}, ${\mathit{t}}_{2}$ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with ${\mathit{t}}_{2}$.

Physical review. B, Condensed matter•Sep 1, 1992•11 citations

Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant

A. Sherman, Michael Schreiber

The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. At half-filling, the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately the results of Monte Carlo simulations. Also, in agreement with numerical simulations, no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\ensuremath{\lesssim}\overline{n}\ensuremath{\lesssim}1.2$ for the repulsion parameters $8\ensuremath{\mid}t\ensuremath{\mid}\ensuremath{\leqslant}U\ensuremath{\leqslant}16\ensuremath{\mid}t\ensuremath{\mid}$. However, for larger $U∕\ensuremath{\mid}t\ensuremath{\mid}$ and $\ensuremath{\mid}1\ensuremath{-}\overline{n}\ensuremath{\mid}\ensuremath{\approx}0.2$, the nearest-neighbor correlations become ferromagnetic. For $\overline{n}\ensuremath{\lesssim}0.94$ and $\overline{n}\ensuremath{\gtrsim}1.06$, the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.

arXiv:0707.0584•Physical Review B•Dec 14, 2007•14 citations
We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping t2{t}_{2}t2​ by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with t2{t}_{2}t2​=0. We discuss the connection of this model to CuO2{\mathrm{CuO}}_{2}CuO2​ planes in the oxide superconductors and the possible implication of our results for these materials.
We have studied the behavior of pairing correlations and susceptibilities in the repulsive Hubbard model on a two-dimensional square lattice by Monte Carlo simulations. Lattice sizes up to 8\ifmmode\times\else\texttimes\fi{}8, temperatures down to T=0.083 (in units where the bandwidth W=8), interaction strengths up to U=16, and several band fillings ranging from (1/2-filled to (1/4-filled were considered. Our results suggest that the model does not exhibit superconductivity. The implications with respect to possible mechanisms for high-Tc{T}_{c}Tc​ superconductivity in oxides are discussed.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping ${\mathit{t}}^{\ensuremath{'}}$=-0.35t as a model for high-temperature superconductors. Magnetic properties are analyzed using the two-particle self-consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite ${\mathit{t}}^{\ensuremath{'}}$ and at ${\mathit{t}}^{\ensuremath{'}}$=0 but for two totally different physical reasons. When ${\mathit{t}}^{\ensuremath{'}}$=0, it is induced by antiferromagnetic correlations while at ${\mathit{t}}^{\ensuremath{'}}$=-0.35t it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with T-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the d-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.
We study the attractive (i.e., negative-U) Hubbard model with nearest (t) and next-nearest-neighbor (t2{\mathit{t}}_{2}t2​) hopping on a square lattice. A spin-down particle-hole transformation maps the negative-U model at any band filling onto a repulsive model with a magnetic field and at zero chemical potential; the sign of the second-neighbor hopping constant in this model depends on the spin state. For large \ensuremath{\Vert}U\ensuremath{\Vert}, t2{\mathit{t}}_{2}t2​ induces a coupling between spin operators in next-nearest-neighbor sites: antiferromagnetic between the z components and ferromagnetic along the transverse direction. The superconducting transition is investigated through Monte Carlo simulations on the attractive model. Fixing both U and the band filling, we find that the critical temperature increases steadily with t2{\mathit{t}}_{2}t2​.
The magnetic susceptibility of the two-dimensional repulsive Hubbard model with nearest-neighbor hopping is investigated using the diagram technique developed for the case of strong correlations. In this technique, a power series in the hopping constant is used. At half-filling, the calculated zero-frequency susceptibility and the square of the site spin reproduce adequately the results of Monte Carlo simulations. Also, in agreement with numerical simulations, no evidence of ferromagnetic correlations was found in the considered range of electron concentrations $0.8\ensuremath{\lesssim}\overline{n}\ensuremath{\lesssim}1.2$ for the repulsion parameters $8\ensuremath{\mid}t\ensuremath{\mid}\ensuremath{\leqslant}U\ensuremath{\leqslant}16\ensuremath{\mid}t\ensuremath{\mid}$. However, for larger $U∕\ensuremath{\mid}t\ensuremath{\mid}$ and $\ensuremath{\mid}1\ensuremath{-}\overline{n}\ensuremath{\mid}\ensuremath{\approx}0.2$, the nearest-neighbor correlations become ferromagnetic. For $\overline{n}\ensuremath{\lesssim}0.94$ and $\overline{n}\ensuremath{\gtrsim}1.06$, the imaginary part of the real-frequency susceptibility becomes incommensurate for small frequencies. The incommensurability parameter grows with departure from half-filling and decreases with increasing frequency. This behavior of the susceptibility can explain the observed low-frequency incommensurate response observed in normal-state lanthanum cuprates.