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

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

Hiromi Otsuka

Published May 15, 1992• 51 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.61.1645

Related papers

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

Effect of Doublon–Holon Binding on Mott Transition–Variational Monte Carlo Study of Two-Dimensional Bose Hubbard Models

Hisatoshi Yokoyama, Tomoaki Miyagawa, Masao Ogata

To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length $ξ_{\rm dh}$ and the minimum D-D exclusion length $ξ_{\rm dd}$. Generally, a Mott transition occurs when $ξ_{\rm dh}$ becomes comparable to $ξ_{\rm dd}$. In the conductive (superfluid) state, domains of D-H pairs overlap with each other ($ξ_{\rm dh}>ξ_{\rm dd}$); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.

arXiv:1104.0516•Journal of the Physical Society of Japan•Aug 15, 2011•27 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

Study of the accuracy of the Gutzwiller wave function for the two-dimensional Hubbard model

X. Q. Hong, J. E. Hirsch

We use a variational Monte Carlo method (VMC) and a quantum Monte Carlo method to study the two-dimensional half-filled Hubbard model. We use the Gutzwiller wave function as a trial wave function in VMC and measure energy, correlation functions, and momentum distribution for lattices up to 12\ifmmode\times\else\texttimes\fi{}12 sites. We then use a Monte Carlo algorithm to study the Hubbard model with the same boundary conditions as in VMC at very low temperatures. By comparing the results from these two methods, we assess the accuracy of the Gutzwiller wave function as a representation of the ground state of the Hubbard model. Major differences are found, implying that the Gutzwiller wave function is not a useful approximation to the ground state of the Hubbard model in two dimensions.

Physical review. B, Condensed matter•Mar 1, 1990•4 citations

Variational Monte-Carlo Studies of Hubbard Model. II

Hisatoshi Yokoyama, Hiroyuki Shiba

As a continuation of a previous paper [J. Phys. Soc. Jpn. 56 (1987) 1490], the variational Monte-Carlo method is extended to include the antiferromagnetic long-range order. The theory is based on the Gutzwiller-type correlation factor and its effect is exactly taken into account by the Monte-Carlo procedure. An application is made to the half-filled-band case of one-dimensional lattice (50 sites), two-dimensional square lattice (up to 20×20 sites) and three-dimensional simple cubic lattice (6×6×6 sites). The result is qualitatively different from previous studies relying on the random-phase-type "Gutzwiller approximation." The variational energy for two and three dimensions is favorably compared with Hirsch's quantum Monte-Carlo data.

Journal of the Physical Society of Japan•Oct 15, 1987•153 citations

Variational Monte Carlo Study of Two-Dimensional Multi-Orbital Hubbard Model on Square Lattice

Y Takenaka, N. Kawakami

We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.

Journal of Physics Conference Series•Dec 17, 2012•5 citations
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.
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.
To understand the mechanism of Mott transitions in case of no magnetic influence, superfluid-insulator (Mott) transitions in the S=0 Bose Hubbard model at unit filling are studied on the square and triangular lattices, using a variational Monte Carlo method. In trial many-body wave functions, we introduce various types of attractive correlation factors between a doubly-occupied site (doublon, D) and an empty site (holon, H), which play a central role for Mott transitions, in addition to the onsite repulsive (Gutzwiller) factor. By optimizing distance-dependent parameters, we study various properties of this type of wave functions. With a hint from the Mott transition arising in a completely D-H bound state, we propose an improved picture of Mott transitions, by introducing two characteristic length scales, the D-H binding length ξdhξ_{\rm dh}ξdh​ and the minimum D-D exclusion length ξddξ_{\rm dd}ξdd​. Generally, a Mott transition occurs when ξdhξ_{\rm dh}ξdh​ becomes comparable to ξddξ_{\rm dd}ξdd​. In the conductive (superfluid) state, domains of D-H pairs overlap with each other (ξdh>ξddξ_{\rm dh}>ξ_{\rm dd}ξdh​>ξdd​); thereby D and H can propagate independently as density carriers by successively exchanging the partners. In contrast, intersite repulsive Jastrow (D-D and H-H) factors have little importance for the Mott transition.
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.
We use a variational Monte Carlo method (VMC) and a quantum Monte Carlo method to study the two-dimensional half-filled Hubbard model. We use the Gutzwiller wave function as a trial wave function in VMC and measure energy, correlation functions, and momentum distribution for lattices up to 12\ifmmode\times\else\texttimes\fi{}12 sites. We then use a Monte Carlo algorithm to study the Hubbard model with the same boundary conditions as in VMC at very low temperatures. By comparing the results from these two methods, we assess the accuracy of the Gutzwiller wave function as a representation of the ground state of the Hubbard model. Major differences are found, implying that the Gutzwiller wave function is not a useful approximation to the ground state of the Hubbard model in two dimensions.
As a continuation of a previous paper [J. Phys. Soc. Jpn. 56 (1987) 1490], the variational Monte-Carlo method is extended to include the antiferromagnetic long-range order. The theory is based on the Gutzwiller-type correlation factor and its effect is exactly taken into account by the Monte-Carlo procedure. An application is made to the half-filled-band case of one-dimensional lattice (50 sites), two-dimensional square lattice (up to 20×20 sites) and three-dimensional simple cubic lattice (6×6×6 sites). The result is qualitatively different from previous studies relying on the random-phase-type "Gutzwiller approximation." The variational energy for two and three dimensions is favorably compared with Hirsch's quantum Monte-Carlo data.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.