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

Molecular Crystals and Liquid Crystals

Charge and magnetic properties of 2D extended Hubbard model

Said Harir, A. Zouhair, Mohamed Bennai, Y. Boughaleb

Published Mar 23, 2016• 2 citations
Publisher

Abstract

The ground state of the two-dimensional Extended Hubbard Model is studied within an exact analytical diagonalization. The Charge and magnetic properties are determined by analyzing the behaviour of charge gap and spin gap as a function of on-site coulomb interaction energy U and spin-spin interaction term J. The obtained results showed that the introduction of long-range off-site interactions induces a vanishing of charge gap and a J independency of spin gap.

DOI
10.1080/15421406.2015.1137123

Related papers

Phase transitions and exact ground-state properties of the one-dimensional Hubbard model in a magnetic field

Chia‐Wei Yang, ARMEN N. KOCHARIAN, Y. L. Chiang

The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.

Journal of Physics Condensed Matter•Aug 2, 2000•24 citations

Charge Gap in One—Dimensional Extended Hubbard Model

DINGGuo-Hui, YEFei

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.

理论物理通讯：英文版•Jan 1, 2003•0 citations

Charge Gap in One-Dimensional Extended Hubbard Model

Guo-Hui Ding, Fei Ye, Xu Bo-wei

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.

Communications in Theoretical Physics•Jan 15, 2003•3 citations

Ground State Energy of 2d Extended Hubbard Model for Finite Size System with AN Exact Diagonalization

Coden Fizae, Said Harir, Mohamed Bennai +1 more

Using an exact analytical diagonalization for an extended Hubbard model, we study the first nearest-neighbour repulsion effect on the behaviour of a two-dimensional system of finite size at low density of electrons. The obtained results show that the introduction of the nearest-neighbour off-site interaction allows the correlation effects to become more remarkable and to play an essential role in the electron dynamics, and this off-site interaction encourages the formation of double occupancies.

FizA•Jan 1, 2008•0 citations

Spin and charge response to magnetic frustration in the Hubbard model

Yang Liu

Unusual normal-state properties of strongly correlated electron materials have been discovered in recent years. They can not be explained by traditional theories. Much work has been devoted to exploring the physical insight into these properties. In the dissertation, the study of spin and charge response to magnetic frustration in the Hubbard Model is presented. Using exact diagonalization techniques, the eigenvalues and eigenvectors of a two-dimensional Hubbard model applied to a cluster with periodic boundary conditions have been obtained. Static and dynamic spin and charge correlation functions as well as one-particle excitation spectra have been calculated. The effects of magnetic frustration due to geometrical competition of different electron hopping terms are studied for various doping and short-range Coulomb interaction parameters. The calculated results are discussed in the framework of many-body physics.

•May 29, 2019•0 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
The ground state of the two-dimensional Extended Hubbard Model is studied within an exact analytical diagonalization. The Charge and magnetic properties are determined by analyzing the behaviour of charge gap and spin gap as a function of on-site coulomb interaction energy U and spin-spin interaction term J. The obtained results showed that the introduction of long-range off-site interactions induces a vanishing of charge gap and a J independency of spin gap.
The exact phase diagrams of the one-dimensional Hubbard model, both attractive and repulsive, in the presence of an arbitrary magnetic field h for various electron concentrations n and on-site interaction strengths U <0 or U >0 are calculated and investigated. The exact ground-state properties, namely, the ground-state energy, the average spin (magnetization), the concentration of the doubly occupied sites, the kinetic energy, the chemical potential, the spin (magnetic) susceptibility and the charge compressibility, are calculated and examined over a wide range of interaction strengths U for various h and n . It is found that the spin susceptibility at half-filling is non-analytic and changes discontinuously as U →0. The exact theory shows the absence of a charge energy gap in the U ⩽0 region for all n and provides, for the chemical potential, the rigorous upper and lower bounds for half-filled and empty bands respectively. The analytical results derived for the weak-coupling limit and asymptotic expansions for strong coupling are in full agreement with the numerical calculations.
Unusual normal-state properties of strongly correlated electron materials have been discovered in recent years. They can not be explained by traditional theories. Much work has been devoted to exploring the physical insight into these properties. In the dissertation, the study of spin and charge response to magnetic frustration in the Hubbard Model is presented. Using exact diagonalization techniques, the eigenvalues and eigenvectors of a two-dimensional Hubbard model applied to a cluster with periodic boundary conditions have been obtained. Static and dynamic spin and charge correlation functions as well as one-particle excitation spectra have been calculated. The effects of magnetic frustration due to geometrical competition of different electron hopping terms are studied for various doping and short-range Coulomb interaction parameters. The calculated results are discussed in the framework of many-body physics.
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.