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Journal of the Physical Society of Japan

Single Band Hubbard Model with Infinite Repulsion on 2×2×2 Lattice

Minoru Takahashi

Published Jul 1, 1979• 7 citations
Publisher

Abstract

All the energy eigenvalues of the Hubbard model with infinite repulsion on 2×2×2 cubic lattice for different electron numbers N e are calculated numerically. For N e =4, 7 the ground state is completely ferromagnetic; namely, total spin S is N e /2. For N e =5, the total spin of the ground state is 3/2. For N e =2, 6, it is zero. For N e =1, 3, it is 1/2. Thermodynamic quantities such as entropy, susceptibility and specific heat are calculated with the method of canonical ensemble. There are two peaks in the specific heat curve for N e =4, 5, 6, 7, but only one peak for N e =1, 2, 3.

DOI
10.1143/jpsj.47.47

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All the energy eigenvalues of the Hubbard model with infinite repulsion on 2×2×2 cubic lattice for different electron numbers N e are calculated numerically. For N e =4, 7 the ground state is completely ferromagnetic; namely, total spin S is N e /2. For N e =5, the total spin of the ground state is 3/2. For N e =2, 6, it is zero. For N e =1, 3, it is 1/2. Thermodynamic quantities such as entropy, susceptibility and specific heat are calculated with the method of canonical ensemble. There are two peaks in the specific heat curve for N e =4, 5, 6, 7, but only one peak for N e =1, 2, 3.
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.
The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.
Abstract. We study the influence of on-site disorder on the magnetic properties of the ground state of the infinite-U one-dimensional (1D) Hubbard model. We find that the ground state is not ferromagnetic. This is analysed in terms of the algebraic structure of the spin dependence of the Hamiltonian. A simple explanation is derived for the 1=N periodicity in the persistent current for this model. The Hubbard model is the simplest model one can study to examine the effects of correlations between electrons in narrow energy bands. The Hamiltonian consists of a nearest neighbour hopping term and an electron–electron repulsion, U, which acts only when two electrons are on the same site. The Hubbard model is also the canonical model for the study of itinerant ferromagnetism. The strong coupling regime is of special importance for the study of ferromagnetism, since a theorem by Nagaoka [1] states that in theU D 1 limit, the ground state (GS) is ferromagnetic given some connectivity property of the lattice (which holds in most cases for d> 1). The model is solvable in one dimension and it was shown [2] that for open boundary conditions (BCs) the GS for finiteU is a singlet, i.e. there can be no ferromagnetism unless one postulates explicitly spin- or velocity-dependent forces. For infinite U, the GS of
In this work we obtain the magnetic and thermodynamic properties of the classical Hubbard model. This one is easier to handle than the original Hubbard model, and it maintains fundamental aspects like charge and particle-hole symmetry. We find the relationship between this and the Ising model. For square and simple cubic lattices, the thermodynamic properties and phase diagrams were calculated by Monte Carlo method. We show the behavior of internal energy, specific heat, and magnetic susceptibility as a function of the temperature. For the considered lattices, the ground state is anti-ferromagnetic. The Néel temperatures were found as a function of the electronic interaction in the case of half-filled band. In the limit of vanishing of diverging interaction, our results agree with the Ising model.