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Soviet Journal of Low Temperature Physics

Magnetic properties of the Hubbard model with an infinite repulsion on a rectangular anisotropic lattice

E. V. Ezerskaya, Vladyslav O. Cheranovskii

Published Aug 1, 1992• 0 citations
Publisher

Abstract

Hubbard’s model with an infinite repulsion on a rectangular anisotropic lattice with Ln-center segments is analyzed. For lattices with L + 1 electrons and cyclic boundary conditions, an exact dependence is obtained between the lattice dimensions and critical values of the Hubbard Hamiltonian parameters at which the ferromagnetic order is violated.

DOI
10.1063/10.0033252

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Hubbard’s model with an infinite repulsion on a rectangular anisotropic lattice with Ln-center segments is analyzed. For lattices with L + 1 electrons and cyclic boundary conditions, an exact dependence is obtained between the lattice dimensions and critical values of the Hubbard Hamiltonian parameters at which the ferromagnetic order is violated.
Low-energy states of the Hubbard model with infinite electron repulsion on an anisotropic triangular strip-type lattice formed by weakly interacting linear segments are studied. The estimates of the stability region boundaries for the ferromagnetic ground state of the lattice are obtained in first order perturbation theory in the interaction between the segments. It is shown that a magnetic transition accompanied by a jumpwise variation of the total spin of the ground state from the minimum to the maximum value is possible for lattices with cyclic boundary conditions and the number of electrons greater than the number of segments by unity.
We study the dependence of the ground state spin of a multiband Hubbard model with infinite electron repulsion on anisotropic triangular and rectangular lattice strips on the model parameters. Considering the results of numerical calculations for the exact spectra of finite triangular lattice strips at different values of hopping integrals, we show the existence of a type of magnetic transitions with the jump of the ground state spin between minimal and maximal values. This transition is found only for special filling factors and when the lattice anisotropy parameter takes some critical value, which depends on the size of the lattice strip. Near this critical point two states with marginal values of the total spin, both of which can be a ground state before or after the transition, are locally stable against a few flips of spins.
The estimations of the stability region of the lattice ferromagnetic ground state in the space of model parameters are found. For the triangular lattice strip formed by L segments with the total number of electrons N=L+1 we derived the effective Hamiltonians describing the low-energy states of the strips and obtained the analytical estimations for above stability region. The possibility of the magnetic transition with the jump of the ground-state spin between minimal and maximal values has also been shown. For the strip with N=L and an alternating value of the one-site potential energy, we have obtained the exact relation between electron parameters, which provides the ferromagnetic character of the lattice ground state. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 253–259, 2001
A Hubbard model with infinite Coulomb repulsion is studied in a many-electron operator representation. A picture of the density of states is constructed using expressions for the one-particle Green’s functions of first order in 1/ z . Its behavior is studied near the Fermi level, especially Condon effects. The stability of saturated ferromagnetism is examined. The corresponding critical current carrier densities are found for semielliptical and rectangular seed densities of state, and for square and cubic lattices. These results are compared with earlier work.
The phase diagrams and electron orderings of the half-filled extended Hubbard models with anisotropic spin-exchange interactions (J⊥, J||) are studied. The cases of ferromagnetic (Jα 0) exchange couplings are considered for repulsive on-site interaction (U ≥ 0). The analysis of these t–U–J||–J⊥ models is performed for d-dimensional hypercubic lattices including d = 1 and d = ∞ by means of the (broken symmetry) HFA supplemented, for d = ∞, by the slave-boson mean-field method. The basic features of the derived phase diagrams are discussed.
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