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

Journal of the Physical Society of Japan

d-Wave State with Multiplicative Correlation Factors for the Hubbard Model

Takashi Yanagisawa, Soh Koike, Yamaji K.

Published Nov 15, 1999• 30 citations
Publisher

Abstract

A d -wave state wave function with multiplicative correlation factors for the Hubbard model is investigated using a variational Monte Carlo method. Employing a simple Gutzwiller-BCS wave function as a starting wave function, we consider improved wave functions with off-diagonal correlation factors. The Monte Carlo simulations are carried out on a square lattice with size 10×10 for U =8 and next nearest neighbor transfer t '=-0.09. The ground-state energy is evaluated from an extrapolation. Our wave functions show that pair correlation functions are enhanced for a negative value of t '.

DOI
10.1143/jpsj.68.3608

Related papers

Off-Diagonal Wave Functions and Superconductivity in the Variational Monte Carlo Calculations.

Takashi Yanagisawa, Takeshi Nakanishi, Soh Koike +1 more

We investigate the two-dimensional Hubbard model by the variational Monte Carlo method. We consider off-diagonal wave functions where we improve the Gutzwiller wave function by multiplying off-diagonal factors. In the 4×4 system, we compare our results with the exact diagonalization. The variational energies are fairly close to the exact values. We show the results for the 10×10 Hubbard model.

The Review of High Pressure Science and Technology•Jan 1, 1998•5 citations

Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model I

Takashi Yanagisawa, Soh Koike, Yamaji K.

We propose a Monte Carlo method, which is a hybrid method of the quantum Monte Carlo method and variational Monte Carlo theory, to study the Hubbard model. The theory is based on the off-diagonal and the Gutzwiller type correlation factors which are taken into account by a Monte Carlo algorithm. In the 4x4 system our method is able to reproduce the exact results obtained by the diagonalization. An application is given to investigate the half-filled band case of two-dimensional square lattice. The energy is favorably compared with quantum Monte Carlo data.

arXiv:cond-mat/0206033•Journal of the Physical Society of Japan•Nov 1, 1998•47 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

Variational Monte-Carlo Studies of Hubbard Model. III. Intersite Correlation Effects

Hisatoshi Yokoyama, Hiroyuki Shiba

New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.

Journal of the Physical Society of Japan•Oct 15, 1990•133 citations

Variational Monte Carlo Studies of the Hubbard Model in One- and Two-Dimensions –Off-Diagonal Intersite Correlation Effects–

Hiromi Otsuka

We investigate the ground state properties of the one- and the two-dimensional Hubbard models using a new variational Monte Carlo method. By generalizing the Gutzwiller variational wave function (GF) to take into account an off-diagonal intersite correlation, we examine the metal-insulator transition mechanism at the half filling. As Kaplan et al. first pointed out, the binding mechanism between doubly occupied sites and empty sites plays a crucial role for this transition; we confirm this by examining the real space correlation function between these two kinds of sites. Results for the spin and the charge structure factors are presented as well as the momentum distribution function and are discussed in connection with the pairing effect. We also find that in less-than half filling, the improvements of the structure factors at 2 k F are realized as compared with GF results.

Journal of the Physical Society of Japan•May 15, 1992•51 citations

Superconductivity and Inhomogeneous Charge-Ordered State in the Two-Dimensional Hubbard Model —Off-Diagonal Wave Function Monte Carlo Studies of Hubbard Model IV—

Takashi Yanagisawa

We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp($-S$)-type where $S$ is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The $d$-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the $d$-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.

arXiv:2506.12736•Journal of the Physical Society of Japan•Jun 20, 2025•0 citations
A d -wave state wave function with multiplicative correlation factors for the Hubbard model is investigated using a variational Monte Carlo method. Employing a simple Gutzwiller-BCS wave function as a starting wave function, we consider improved wave functions with off-diagonal correlation factors. The Monte Carlo simulations are carried out on a square lattice with size 10×10 for U =8 and next nearest neighbor transfer t '=-0.09. The ground-state energy is evaluated from an extrapolation. Our wave functions show that pair correlation functions are enhanced for a negative value of t '.
We propose a Monte Carlo method, which is a hybrid method of the quantum Monte Carlo method and variational Monte Carlo theory, to study the Hubbard model. The theory is based on the off-diagonal and the Gutzwiller type correlation factors which are taken into account by a Monte Carlo algorithm. In the 4x4 system our method is able to reproduce the exact results obtained by the diagonalization. An application is given to investigate the half-filled band case of two-dimensional square lattice. The energy is favorably compared with quantum Monte Carlo data.
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.
New variational wave functions are introduced to describe the Hubbard model in strong correlation. Intersite correlation (or Jastrow) factors are taken into account beyond the Gutzwiller wave function (GF). A study is made on the one-dimensional lattice and the two-dimensional square lattice at half-filling as well as less-than-half-filling. Much improvement can be achieved thereby in the description of physical quantities such as the momentum distribution and spin and charge density correlation functions. In addition, the ground state energy is lowered appreciably compared with the GF. In this connection, the Mott-Hubbard-type metal-insulator transition is also re-examined.
We investigate the ground state properties of the one- and the two-dimensional Hubbard models using a new variational Monte Carlo method. By generalizing the Gutzwiller variational wave function (GF) to take into account an off-diagonal intersite correlation, we examine the metal-insulator transition mechanism at the half filling. As Kaplan et al. first pointed out, the binding mechanism between doubly occupied sites and empty sites plays a crucial role for this transition; we confirm this by examining the real space correlation function between these two kinds of sites. Results for the spin and the charge structure factors are presented as well as the momentum distribution function and are discussed in connection with the pairing effect. We also find that in less-than half filling, the improvements of the structure factors at 2 k F are realized as compared with GF results.
We investigate the ground-state properties of the two-dimensional Hubbard model, based on the off-diagonal wave function variational Monte Carlo method. We use an optimized wave function that is improved from an initial one-body wave function by multiplying by multiple correlation operators that are given by the form of exp(−S-S−S)-type where SSS is a suitable operator. We examine the inhomogeneous ground state at near 1/8 doping in the strongly correlated region where the on-site Coulomb interaction is larger than the bandwidth. The ddd-wave superconductivity with a spatially oscillating gap function can coexist with the charge ordering in the ground state without magnetic ordering, and superconducting condensation energy increases by this coexistence. We also show the ddd-wave pair correlation function as a function of lattice sites. The correlation function indicates that the long-range superconducting order indeed exists, and also that the strong electron correlation suppresses the pair correlation function.