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 Astrophysics & Aerospace Technology

Correlation between Lanczos Method and Exact Diagonalisation Method in the Study of Highly Correlated Electrons System

Michael Obende Okanigbuan OR

Published Jan 1, 2015• 0 citations
Publisher

Abstract

The ground state energy and wave function of the single band hubbard model on the one dimensional lattice is computed using the Lanczos methods. It is shown that the ground state energies obtained for different values of the interaction strength it, compare nicely with that obtained using the method of exact calculation.
DOI
10.4172/2329-6542.1000113

Related papers

Correlation between perturbation and variation methods in the study of strongly correlated electron systems

Robinson O. Okanigbuan, JO Idiodi

The ground–state wave function and energy are calculated for two electrons subject to a one-band Hubbard Hamiltonian on a one dimensional lattice containing N electronic sites, N = 2,3,4,5,6, and a 3 x 3 cluster of the square lattice, using perturbation and variational methods. The results from these two approximation methods are then compared with the result from exact calculational method. Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 583-594

Journal of the Nigerian Association of Mathematical Physics•May 22, 2008•0 citations

Electron Interaction at Low Filling in Two Dimensions Using a Simplification of the Modified Lanczos Technique

E. O. Osafile, D.O. Ojuh, Joa Idiodi

In this paper, a detailed study of the dynamics of the behavior of two electrons in two dimensions is carried out. Over the years, the Hubbard model has been heavily used as one of the standard models for the study of strongly correlated electron systems. Despite this, the mechanism of interaction of these electrons in two- dimensional systems is yet to be properly understood. Based on this clarity problem, a modification of the standard Lanczos algorithm which is slightly different, simpler and more analytical than that presented by Dagotto in his review paper is used in a concerted attempt to produce relevant results for the correlated ground state energies and wave functions and the behavior of the interacting pairs is explained with the aid of the well known single band Hubbard model. Hence this study has been able to develop, stabilize and utilize a simplified modification of the standard Lanczos technique. From results obtained, for large and positive values of u, interaction is repulsive while it is attractive for negative values of u. The wave function can be readily obtained at the end of each step of iteration.

Greener Journal of Science Engineering and Technological Research•Apr 20, 2013•0 citations

Application of density matrix renormalization group to one-dimensional Hubbard model to study strongly correlated electrons system

Olusanmi Ebenezer Odeyemi, Akinola Samson Olayinka, Arthur Imooah Ejere +3 more

In this work, we applied density matrix renormalization group to one-dimensional Hubbard model at five numbers of sweep to solve strongly correlated interacting electrons system, starting from two electrons on two sites up to ten electrons on ten sites at half filling. The results that emerged from the present study is in agreement with that of exact diagonalization, variational and Lanczos solution at the varying values of the Coulomb interaction strength (U/t) at t=1. The total energy, Eg/t, of the ground state increases with the increase in interaction strength for all the numbers of site, N. The spectra intensity increases with increase in the interaction strength but decreases to zero when the interaction strength is made negatively large. This study is extended to more than two electrons on two sites. We equally show effect of interaction strength, U/t, at t = 1 on the energy-dependent entropy, S. Key words: Density matrix renormalization group, Hubbard model, sweep, exact diagonalization, variational, Lanczos, entropy.

International Journal of the Physical Sciences•Jun 12, 2019•0 citations

Interaction-energy functional for lattice density functional theory: Applications to one-, two-, and three-dimensional Hubbard models

Román López-Sandoval, G. M. Pastor

The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix ${\ensuremath{\gamma}}_{\mathrm{ij}}$ with respect to the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\ensuremath{\gamma}]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of W is obtained throughout the domain of representability of ${\ensuremath{\gamma}}_{\mathrm{ij}},$ including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for W. Goals and limitations of the different approximations are discussed.

arXiv:cond-mat/0311470•Physical Review B•Feb 13, 2004•29 citations

Analysis of Electron Correlation in the Modified Single-band Hubbard Model

Edison A. Enaibe, Akpata Erhieyovwe, Nelson Oyindenyifa Nenuwe

The major characteristic of the single-band Hubbard model (HM) is to redistribute electrons at a uniform lattice separation distance within the molecular lattice. Hence, it is only linearly dependent on lattice separations distance. Thus the single-band Hubbard model does not consider the lattice gradient encountered by interacting electrons as they hop from one lattice point to another. The linear dependence of the single-band HM only on lattice separations would certainly not provide a thorough understanding of the interplay between interacting electrons. Consequently, we have in this study developed a gradient Hamiltonian model to solve the associated defects pose by the limitations of the single band Hubbard model. Thus, we utilized the single-band HM and the gradient Hamiltonian model to study the behaviour of two interacting electrons on a two dimensional (2D) 9X9 square lattice. It is revealed in this study that the results of the ground-state energies produced by the gradient Hamiltonian model are more favourable when compared to those of the single-band Hubbard model. We have also shown in this work, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.

Physical Science International Journal•Jan 10, 2016•0 citations

Exact calculation of the two-electron interaction in the ground state of the Hubbard model

Liang Chen, Changjiang Mei

The single-band Hubbard model has been studied in both the one-dimensional ring and two-dimensional torus. By the exact calculation of the pair correlation function F(i,j), defined as the possibility of finding an electron at site j when there has been an electron at site i, it is shown that for two electrons, the interaction is always repulsive in the ground state for any positive value of the on-site Coulomb interaction U.

Physical review. B, Condensed matter•May 1, 1989•18 citations
In this paper, a detailed study of the dynamics of the behavior of two electrons in two dimensions is carried out. Over the years, the Hubbard model has been heavily used as one of the standard models for the study of strongly correlated electron systems. Despite this, the mechanism of interaction of these electrons in two- dimensional systems is yet to be properly understood. Based on this clarity problem, a modification of the standard Lanczos algorithm which is slightly different, simpler and more analytical than that presented by Dagotto in his review paper is used in a concerted attempt to produce relevant results for the correlated ground state energies and wave functions and the behavior of the interacting pairs is explained with the aid of the well known single band Hubbard model. Hence this study has been able to develop, stabilize and utilize a simplified modification of the standard Lanczos technique. From results obtained, for large and positive values of u, interaction is repulsive while it is attractive for negative values of u. The wave function can be readily obtained at the end of each step of iteration.
In this work, we applied density matrix renormalization group to one-dimensional Hubbard model at five numbers of sweep to solve strongly correlated interacting electrons system, starting from two electrons on two sites up to ten electrons on ten sites at half filling. The results that emerged from the present study is in agreement with that of exact diagonalization, variational and Lanczos solution at the varying values of the Coulomb interaction strength (U/t) at t=1. The total energy, Eg/t, of the ground state increases with the increase in interaction strength for all the numbers of site, N. The spectra intensity increases with increase in the interaction strength but decreases to zero when the interaction strength is made negatively large. This study is extended to more than two electrons on two sites. We equally show effect of interaction strength, U/t, at t = 1 on the energy-dependent entropy, S. Key words: Density matrix renormalization group, Hubbard model, sweep, exact diagonalization, variational, Lanczos, entropy.
The Hubbard model is investigated in the framework of lattice density functional theory (LDFT). The single-particle density matrix ${\ensuremath{\gamma}}_{\mathrm{ij}}$ with respect to the lattice sites is considered as the basic variable of the many-body problem. A new approximation to the interaction-energy functional $W[\ensuremath{\gamma}]$ is proposed which is based on its scaling properties and which recovers exactly the limit of strong electron correlations at half-band filling. In this way, a more accurate description of W is obtained throughout the domain of representability of ${\ensuremath{\gamma}}_{\mathrm{ij}},$ including the crossover from weak to strong correlations. As examples of applications results are given for the ground-state energy, charge-excitation gap, and charge susceptibility of the Hubbard model in one-, two-, and three-dimensional lattices. The performance of the method is demonstrated by comparison with available exact solutions, with numerical calculations, and with LDFT using a simpler dimer ansatz for W. Goals and limitations of the different approximations are discussed.
The major characteristic of the single-band Hubbard model (HM) is to redistribute electrons at a uniform lattice separation distance within the molecular lattice. Hence, it is only linearly dependent on lattice separations distance. Thus the single-band Hubbard model does not consider the lattice gradient encountered by interacting electrons as they hop from one lattice point to another. The linear dependence of the single-band HM only on lattice separations would certainly not provide a thorough understanding of the interplay between interacting electrons. Consequently, we have in this study developed a gradient Hamiltonian model to solve the associated defects pose by the limitations of the single band Hubbard model. Thus, we utilized the single-band HM and the gradient Hamiltonian model to study the behaviour of two interacting electrons on a two dimensional (2D) 9X9 square lattice. It is revealed in this study that the results of the ground-state energies produced by the gradient Hamiltonian model are more favourable when compared to those of the single-band Hubbard model. We have also shown in this work, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.