EQSE Diagonalization of the Hubbard Model

Nathan Salwen

Published Jan 1, 2000• 0 citations

Abstract

The application of enhanced quasi-sparse eigenvector methods (EQSE) to the Hubbard model is attempted. The ground state energy for the 4x4 Hubbard model is calculated with a relatively small set of basis vectors. The results agree to high precision with the exact answer. For the 8x8 case, exact answers are not available but a simple first order correction to the quasi-sparse eigenvector (QSE) result is presented. 1

Related papers

The exact diagonalization of the extended Hubbard Model: Six Electrons at Half-Filling

Ayomide Emmanuel Adesiyan, Kingsley N. Onaiwu

This study has used the exact diagonalization technique to examine the Extended Hubbard model.The basis vectors were first generated using binary integers available in matlab,the Hamiltonian matrix were subsequently generated using the basis vectors,after-which the Eigen values of the low and some highest laying states were obtained. The results obtained would serve as a good reference against which other results obtained from other approximation techniques can be compared .

Feb 24, 20220 citations

Ground-state energy of the Hubbard model: Cluster-perturbative results

Maciej M. Maśka

When electron correlations are important it is often necessary to use numerical methods to solve the Hamiltonian for a finite system (cluster) ``exactly.'' Unfortunately, such methods are restricted to small systems. We propose to combine the ``exact'' numerical diagonalization for small clusters with the perturbative calculations to take into account the intracluster as well as intercluster interactions.

arXiv:cond-mat/9802171Physical review. B, Condensed matterApr 15, 19987 citations

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

Takashi Yanagisawa, Soh Koike, Yamaji K.

arXiv:cond-mat/0206033Journal of the Physical Society of JapanNov 1, 199847 citations

Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

J. Vučičević, J. Kokalj, Rok Žitko +3 more

arXiv:1811.08343Physical Review LettersJul 19, 201985 citations

GROUND-STATE ENERGY OF THE ONE-DIMENSIONAL HUBBARD MODEL IN A SIMPLE SELF-CONSISTENT VERSION OF THE LADDER APPROXIMATION

Florin D. Buzatu

The ground-state energy of the one-dimensional Hubbard model is calculated within the ladder approximation; from the comparison with the exact results in the repulsive case, it follows that the approximation is good at low densities or small couplings. The ladder approximation can be improved by imposing a self-consistency condition; using a simple assumption, the results become close to the exact ones in a large range of the model parameters.

Modern Physics Letters BAug 10, 19957 citations

Application of the finite-cell-scaling method to the one-dimensional Hubbard model

B. Fourcade, G. Spronken

Physical review. B, Condensed matterMay 1, 198413 citations

EQSE Diagonalization of the Hubbard Model

Nathan Salwen

Published Jan 1, 2000• 0 citations

OpenAlex

Abstract

Related papers

The exact diagonalization of the extended Hubbard Model: Six Electrons at Half-Filling

Ayomide Emmanuel Adesiyan, Kingsley N. Onaiwu

Feb 24, 20220 citations

Ground-state energy of the Hubbard model: Cluster-perturbative results

Maciej M. Maśka

arXiv:cond-mat/9802171Physical review. B, Condensed matterApr 15, 19987 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.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/0206033Journal of the Physical Society of JapanNov 1, 199847 citations

Conductivity in the Square Lattice Hubbard Model at High Temperatures: Importance of Vertex Corrections

J. Vučičević, J. Kokalj, Rok Žitko +3 more

Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results, and the question of the exact solution for the conductivity in the Hubbard model remained open. In this Letter, we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity and identify the best available result to be compared to experiment. We find that, at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4×4, and the corresponding Lanczos diagonalization result is, therefore, close to the exact result in the thermodynamic limit.Recent experiments on cold atoms in optical lattices allow for a quantitative comparison of the measurements to the conductivity calculations in the square lattice Hubbard model. However, the available calculations do not give consistent results, and the question of the exact solution for the conductivity in the Hubbard model remained open. In this Letter, we employ several complementary state-of-the-art numerical methods to disentangle various contributions to conductivity and identify the best available result to be compared to experiment. We find that, at relevant (high) temperatures, the self-energy is practically local, yet the vertex corrections remain rather important, contrary to expectations. The finite-size effects are small even at the lattice size 4×4, and the corresponding Lanczos diagonalization result is, therefore, close to the exact result in the thermodynamic limit.

arXiv:1811.08343Physical Review LettersJul 19, 201985 citations

GROUND-STATE ENERGY OF THE ONE-DIMENSIONAL HUBBARD MODEL IN A SIMPLE SELF-CONSISTENT VERSION OF THE LADDER APPROXIMATION

Florin D. Buzatu

Modern Physics Letters BAug 10, 19957 citations

Application of the finite-cell-scaling method to the one-dimensional Hubbard model

B. Fourcade, G. Spronken

The finite-cell-scaling method is applied to the one-dimensional Hubbard model. In the half-filled-band case and at zero temperature, the numerical results obtained for the ground-state energy differ from the exact solution by approximately 1%. For the range $1<\frac{U}{t}<5$ , where $U$ is the Coulomb interaction and $t$ is the transfer integral, the value of the normalized gap $\frac{\ensuremath{\Delta}}{t}$ agrees well with the exact result while it differs significantly for $0.2<\frac{U}{t}<0.9$ . For the latter range, we show that the gap varies as ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}[{(a+\frac{\mathrm{bU}}{t})}^{\ensuremath{-}1}]$, where $a$ and $b$ are negative constants which depend on the size of the system, instead of ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}(\frac{\ensuremath{-}2\ensuremath{\pi}t}{U})$ as in the exact solution.The finite-cell-scaling method is applied to the one-dimensional Hubbard model. In the half-filled-band case and at zero temperature, the numerical results obtained for the ground-state energy differ from the exact solution by approximately 1%. For the range $1<\frac{U}{t}<5$, where $U$ is the Coulomb interaction and $t$ is the transfer integral, the value of the normalized gap $\frac{\ensuremath{\Delta}}{t}$ agrees well with the exact result while it differs significantly for $0.2<\frac{U}{t}<0.9$. For the latter range, we show that the gap varies as ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}[{(a+\frac{\mathrm{bU}}{t})}^{\ensuremath{-}1}]$, where $a$ and $b$ are negative constants which depend on the size of the system, instead of ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}(\frac{\ensuremath{-}2\ensuremath{\pi}t}{U})$ as in the exact solution.

Physical review. B, Condensed matterMay 1, 198413 citations

1<\frac{U}{t}<5

, where

U

is the Coulomb interaction and

t

is the transfer integral, the value of the normalized gap $\frac{\ensuremath{\Delta}}{t}$ agrees well with the exact result while it differs significantly for

0.2<\frac{U}{t}<0.9

. For the latter range, we show that the gap varies as ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}[{(a+\frac{\mathrm{bU}}{t})}^{\ensuremath{-}1}]$, where

a

and

b

are negative constants which depend on the size of the system, instead of ${(\frac{U}{t})}^{\frac{1}{2}}\mathrm{exp}(\frac{\ensuremath{-}2\ensuremath{\pi}t}{U})$ as in the exact solution.