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

International Journal of Modern Physics B

An Investigation of the Electron Transfer and Repulsive Coulomb Interactions in the One-, Two-, Three-Dimensional Isotropic Hubbard Models I: Eigenfunctions and Eigenvalues

J.M. Dixon, Jack A. Tuszyński

Published Oct 10, 1998• 0 citations
Publisher

Abstract

In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filling factors using examples in one- and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monté Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.

DOI
10.1142/s0217979298001484

Related papers

An investigation of the electron transfer and repulsive Coulomb interactions in the one, two-, three-dimensional isotropic Hubbard models - I: Eigenfunctions and eigenvalues

No author provided

In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filing factors using examples in one- and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monte Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.

•Sep 10, 2026•0 citations

An investigation of the electron transfer and repulsive Coulomb interactions in the one-, two-, three-dimensional isotropic Hubbard models - II: Extension to a Wannier and higher angular momentum basis

No author provided

In the previous paper we have investigated the isotropic Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices. The method involved the determination of the one-electron energies and eigenfunctions of the transfer interaction, the latter being utilised to form determinantal eigenfunctions for the many-electron system as a whole. In this paper we have examined the consequences of using an atomic basis by introducing; Wannier functions and studied physical consequences of this more exact approach. To reduce the transformed two-body interaction to manageable form we have used the rotational properties of individual atomic orbitals incorporating them via irreducible tensorial methods. We find that, although additional components due to Wannier "tails" are small they may modify the nearest neighbor transfer terms significantly and also introduce next-nearest and next-next nearest neighbor transfer interactions. We have also investigated the effect of using atomic orbitals with a higher angular momentum on each site. Both p-orbitals and d-orbitals have been studied and the broad conclusion is that the corresponding Hubbard model reduces to a series of S-like orbital models, one for each component, m, of the degenerate set on each site. The transfer interaction in each case becomes, in general, m dependent, each m component being effectively decoupled from others.

•Sep 10, 2026•0 citations

An Investigation of the Electron Transfer and Repulsive Coulomb Interactions in the One-, Two-, Three-Dimensional Isotropic Hubbard Models II: Extension to a Wannier and Higher Angular Momentum Basis

J.M. Dixon, Jack A. Tuszyński

In the previous paper we have investigated the isotropic Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices. The method involved the determination of the one-electron energies and eigenfunctions of the transfer interaction, the latter being utilised to form determinantal eigenfunctions for the many-electron system as a whole. In this paper we have examined the consequences of using an atomic basis by introducing Wannier functions and studied physical consequences of this more exact approach. To reduce the transformed two-body interaction to manageable form we have used the rotational properties of individual atomic orbitals incorporating them via irreducible tensorial methods. We find that, although additional components due to Wannier "tails" are small they may modify the nearest neighbor transfer terms significantly and also introduce next-nearest and next-next nearest neighbor transfer interactions. We have also investigated the effect of using atomic orbitals with a higher angular momentum on each site. Both p-orbitals and d-orbitals have been studied and the broad conclusion is that the corresponding Hubbard model reduces to a series of S-like orbital models, one for each component, m, of the degenerate set on each site. The transfer interaction in each case becomes, in general, m dependent, each m component being effectively decoupled from others.

International Journal of Modern Physics B•Oct 10, 1998•1 citation

A new algorithm for investigating strongly correlated systems using Hubbard model

Poorya Rabi-‌‌beigi, Rostam Moradian

Abstract In this work for an interacting electrons system that obeys the Hubbard model, a new quantum Monte Carlo algorithm introduces for calculation of average Green function. This algorithm is applied to investigate the effects of electrons onsite Coulomb repulsion on the band structure of a square lattice in both single-site approximations such as dynamical mean field theory (DMFT) and multi-site approximations such as effective medium supercell approximation (EMSCA). The advantages of our algorithm in comparison to the Hirsch-Fye algorithm and also the Blankenbecler, Scalapino, and Sugar (BSS) algorithm are the elimination of instabilities resulting from the Metropolis algorithm in the accepting and rejecting configurations, stability at low temperatures, the elimination of systematic errors resulting from the update of the Green's function in the quantum Monte Carlo process, and considering different probabilities for each possible configuration. Finally, by using our algorithm, it is possible to calculate the interacting three-dimensional system's band structure and the density of states that obey the Hubbard model. We have applied our algorithm to an interactive two-dimensional square lattice. As a result, phase transition boundaries can be easily recognized through calculated bands for different repulsions. Our results show that critical Coulomb repulsion values for Mott transition are uc=9.05t and uc=2.4t for DMFT and BEMSCA respectively. This means that DMFT significantly overestimates band splitting due to electrons' Coulomb repulsion. We found by starting at low repulsions and then increasing electrons' Coulomb repulsion, a partially flatted valance band around the center of the first Brillouin zone appears, but disappears at high repulsions.

•May 26, 2023•0 citations

Phase separation in the two-dimensional Hubbard model

Gang Su

By making use of known exact results and symmetry properties for the one-band Hubbard model, we show in a somewhat exact manner that there is no phase separation on a square lattice at arbitrary fillings at finite temperature for both attractive and repulsive on-site Coulomb interaction. This result is consistent with the quantum Monto Carlo calculation.

arXiv:cond-mat/9609152•Physical review. B, Condensed matter•Sep 15, 1996•23 citations

Electron correlation in a three dimensional cluster of the cubic lattice

Edison A. Enaibe, J. O. A. Idiodi

We study the one-band Hubbard model in a three dimensional simple cubic lattice, with periodic boundary conditions, by means of a variational analytic approach. Ground state energies and pairing correlations depend implicitly on the interaction strength (U/41). 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. Implications of this result for superconductivity are also discussed. Nigerian Journal of Physics Vol. 16(2) 2004: 167-171

Nigerian Journal of Physics•Oct 18, 2006•0 citations
In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filling factors using examples in one- and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monté Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.
In this paper we investigate the Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices with arbitrary values of transfer and on-site repulsion parameters. The method of diagonalization is based on equivalences due to Stevens for number conserving operators and a unitary transformation utilizing permutational symmetries of the problem. We obtained simple analytical formulas for single particle eigenstates and somewhat more involved expression for determinantal multi-electron states. Numerical calculations have been performed which demonstrate the boundaries of the lowest band for various filing factors using examples in one- and two-dimensions. The states within the band have also been identified and degeneracies evaluated numerically. These computations were based on a Monte Carlo technique in conjunction with particle conservation requirements. Agreement with some well-known limiting cases has been found.
In the previous paper we have investigated the isotropic Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices. The method involved the determination of the one-electron energies and eigenfunctions of the transfer interaction, the latter being utilised to form determinantal eigenfunctions for the many-electron system as a whole. In this paper we have examined the consequences of using an atomic basis by introducing; Wannier functions and studied physical consequences of this more exact approach. To reduce the transformed two-body interaction to manageable form we have used the rotational properties of individual atomic orbitals incorporating them via irreducible tensorial methods. We find that, although additional components due to Wannier "tails" are small they may modify the nearest neighbor transfer terms significantly and also introduce next-nearest and next-next nearest neighbor transfer interactions. We have also investigated the effect of using atomic orbitals with a higher angular momentum on each site. Both p-orbitals and d-orbitals have been studied and the broad conclusion is that the corresponding Hubbard model reduces to a series of S-like orbital models, one for each component, m, of the degenerate set on each site. The transfer interaction in each case becomes, in general, m dependent, each m component being effectively decoupled from others.
In the previous paper we have investigated the isotropic Hubbard model, with S-orbits on each site, for one-, two- and three-dimensional isotropic lattices. The method involved the determination of the one-electron energies and eigenfunctions of the transfer interaction, the latter being utilised to form determinantal eigenfunctions for the many-electron system as a whole. In this paper we have examined the consequences of using an atomic basis by introducing Wannier functions and studied physical consequences of this more exact approach. To reduce the transformed two-body interaction to manageable form we have used the rotational properties of individual atomic orbitals incorporating them via irreducible tensorial methods. We find that, although additional components due to Wannier "tails" are small they may modify the nearest neighbor transfer terms significantly and also introduce next-nearest and next-next nearest neighbor transfer interactions. We have also investigated the effect of using atomic orbitals with a higher angular momentum on each site. Both p-orbitals and d-orbitals have been studied and the broad conclusion is that the corresponding Hubbard model reduces to a series of S-like orbital models, one for each component, m, of the degenerate set on each site. The transfer interaction in each case becomes, in general, m dependent, each m component being effectively decoupled from others.
Abstract In this work for an interacting electrons system that obeys the Hubbard model, a new quantum Monte Carlo algorithm introduces for calculation of average Green function. This algorithm is applied to investigate the effects of electrons onsite Coulomb repulsion on the band structure of a square lattice in both single-site approximations such as dynamical mean field theory (DMFT) and multi-site approximations such as effective medium supercell approximation (EMSCA). The advantages of our algorithm in comparison to the Hirsch-Fye algorithm and also the Blankenbecler, Scalapino, and Sugar (BSS) algorithm are the elimination of instabilities resulting from the Metropolis algorithm in the accepting and rejecting configurations, stability at low temperatures, the elimination of systematic errors resulting from the update of the Green's function in the quantum Monte Carlo process, and considering different probabilities for each possible configuration. Finally, by using our algorithm, it is possible to calculate the interacting three-dimensional system's band structure and the density of states that obey the Hubbard model. We have applied our algorithm to an interactive two-dimensional square lattice. As a result, phase transition boundaries can be easily recognized through calculated bands for different repulsions. Our results show that critical Coulomb repulsion values for Mott transition are uc=9.05t and uc=2.4t for DMFT and BEMSCA respectively. This means that DMFT significantly overestimates band splitting due to electrons' Coulomb repulsion. We found by starting at low repulsions and then increasing electrons' Coulomb repulsion, a partially flatted valance band around the center of the first Brillouin zone appears, but disappears at high repulsions.
We study the one-band Hubbard model in a three dimensional simple cubic lattice, with periodic boundary conditions, by means of a variational analytic approach. Ground state energies and pairing correlations depend implicitly on the interaction strength (U/41). 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. Implications of this result for superconductivity are also discussed. Nigerian Journal of Physics Vol. 16(2) 2004: 167-171