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

APS

Low-energy properties of the two-dimensional Hubbard model near half filling

Barry Friedman, Greg Levine

Published Mar 1, 1996• 0 citations
OpenAlex

Abstract

In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4{ital t} of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended {ital s}- and {ital d}-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the {ital d}-wave correlation function, that is, {ital d}-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.

Related papers

Low-energy properties of the two-dimensional Hubbard model near half filling

Barry Friedman, Greg Levine

In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4t of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended s- and d-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the d-wave correlation function, that is, d-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.

Physical review. B, Condensed matter•Oct 15, 1995•1 citation

Configuration-interaction approach to the two-dimensional Hubbard model near half-filling

Barry Friedman, Gregory Levine

The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.

Physical review. B, Condensed matter•Apr 15, 1997•4 citations

Cutoff dependence of a configuration-interaction approach to the two-dimensional Hubbard model

Barry Friedman, Gregory Levine

The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method with kinetic energy cutoffs of $4t,$ $5t,$ and $6t.$ D-wave superconducting order parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. These calculations do not show indications of d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model for the $5t$ and $6t$ cutoffs. To understand these results, in particular the enhancement of d-wave correlations at a cutoff of $4t,$ we implement a different cutoff scheme. In this second scheme we introduce a cutoff in the single particle energies relative to the Fermi surface. Using this second scheme, we obtain a significant enhancement for g-wave superconductivity.

Physical review. B, Condensed matter•Dec 15, 2000•0 citations

Numerical study of the two-dimensional Hubbard model

Steven R. White, Douglas J. Scalapino, Robert L. Sugar +3 more

We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.

Physical review. B, Condensed matter•Jul 1, 1989•947 citations

Antiferromagnetism of the two-dimensional Hubbard model at half-filling: the analytic ground state for weak coupling

Michele Cini, Gianluca Stefanucci

We introduce a local formalism to deal with the Hubbard model on an N × N square lattice (for even N ) in terms of eigenstates of number operators, having well defined point symmetry. For U →0, the low-lying shells of the kinetic energy are filled in the ground state. At half-filling, using the 2 N -2 one-body states of the partially occupied shell hf , we build a set of degenerate unperturbed ground states with S z = 0 which are then resolved by the Hubbard interaction Ŵ = U ∑ r r ↑ r ↓ . We study the many-body eigenstates in hf of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion ( W = 0 states). In the S z = 0 sector, this is an N -times-degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U = 0 + , which is unique, in agreement with a theorem of Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N /2, respectively.

arXiv:cond-mat/0009058•Journal of Physics Condensed Matter•Jan 25, 2001•2 citations

Superconducting Correlationof Two-Dimensional Hubbard Model near Half-Filling

Masatoshi Imada

Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12×12 lattice away from the half-filling and up to 16×16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s - nor d -wave superconducting state is possible in the two-dimensional Hubbard model.

Journal of the Physical Society of Japan•Aug 15, 1991•36 citations
In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4{ital t} of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended {ital s}- and {ital d}-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the {ital d}-wave correlation function, that is, {ital d}-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.
In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4t of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended s- and d-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the d-wave correlation function, that is, d-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method. Superconducting order-parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. Consistent with our previous results, these more extensive calculations point toward d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model. The d-wave correlations tend to increase with interaction strength, size of the state space used in the calculation, and doping away from half-filling. The superconducting correlations on the Fermi surface are interpreted as d-wave pairing between spin density-wave quasiparticles.
The two-dimensional Hubbard model near half-filling is studied using a configuration-interaction method with kinetic energy cutoffs of 4t,4t,4t, 5t,5t,5t, and 6t.6t.6t. D-wave superconducting order parameter and spin-spin correlation functions are calculated as functions of distance to probe for superconductivity and antiferromagnetism. These calculations do not show indications of d-wave superconductivity in the ground state of the two-dimensional repulsive Hubbard model for the 5t5t5t and 6t6t6t cutoffs. To understand these results, in particular the enhancement of d-wave correlations at a cutoff of 4t,4t,4t, we implement a different cutoff scheme. In this second scheme we introduce a cutoff in the single particle energies relative to the Fermi surface. Using this second scheme, we obtain a significant enhancement for g-wave superconductivity.
We report on a numerical study of the two-dimensional Hubbard model and describe two new algorithms for the simulation of many-electron systems. These algorithms allow one to carry out simulations within the grand canonical ensemble at significantly lower temperatures than had previously been obtained and to calculate ground-state properties with fixed numbers of electrons. We present results for the two-dimensional Hubbard model with half- and quarter-filled bands. Our results support the existence of long-range antiferromagnetic order in the ground state at half-filling and its absence at quarter-filling. Results for the magnetic susceptibility and the momentum occupation along with an upper bound to the spin-wave spectrum are given. We find evidence for an attractive effective d-wave pairing interaction near half-filling but have not found evidence for a phase transition to a superconducting state.
We introduce a local formalism to deal with the Hubbard model on an N × N square lattice (for even N ) in terms of eigenstates of number operators, having well defined point symmetry. For U →0, the low-lying shells of the kinetic energy are filled in the ground state. At half-filling, using the 2 N -2 one-body states of the partially occupied shell hf , we build a set of degenerate unperturbed ground states with S z = 0 which are then resolved by the Hubbard interaction Ŵ = U ∑ r r ↑ r ↓ . We study the many-body eigenstates in hf of the kinetic energy with vanishing eigenvalue of the Hubbard repulsion ( W = 0 states). In the S z = 0 sector, this is an N -times-degenerate multiplet. From the singlet component one obtains the ground state of the Hubbard model for U = 0 + , which is unique, in agreement with a theorem of Lieb. The wave function demonstrates an antiferromagnetic order, a lattice step translation being equivalent to a spin flip. We show that the total momentum vanishes, while the point symmetry is s or d for even or odd N /2, respectively.
Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12×12 lattice away from the half-filling and up to 16×16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s - nor d -wave superconducting state is possible in the two-dimensional Hubbard model.