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Absence of Highest-Spin Ground States in the Hubbard Model

O Springer-Verlag

Published Jan 1, 1991• 0 citations
OpenAlex

Abstract

The Hubbard model H = - t Zc~,cr, + U Xn~T n~, with N electrons and periodic boundary condition is studied on v-dimensional L~ x .-. x L~ lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) 7/~ (v > 2) at low electron densities; with one hole if t > 0 and L~ is odd for some i; with two holes if t 0 and all the L~ are even. (ii) The bcc lattice at low densities; with two holes if t 0 and all the L~ are even; with 2 ..... 6 holes if L~ = Land t 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t 0; with two holes if t < 0. Some results for the one dimensional model are also presented.

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The Hubbard model H = - t Zc~,cr, + U XnT n, with N electrons and periodic boundary condition is studied on v-dimensional L~ x .-. x L~ lattices. It is shown that for any value of U there is no ground state with maximal spin (S = N/2) in the following cases: (i) 7/~ (v > 2) at low electron densities; with one hole if t > 0 and L~ is odd for some i; with two holes if t 0 and all the L~ are even. (ii) The bcc lattice at low densities; with two holes if t 0 and all the L~ are even; with 2 ..... 6 holes if L~ = Land t 0 and L is even. (iii) The triangular lattice at densities near 0 and 1 if t > 0; with two holes if t 0; with two holes if t < 0. Some results for the one dimensional model are also presented.
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
We investigate magnetic properties in the ground state of the one-dimensional flat-band Hubbard model in high electron filling. Until now, we found the new saturated ferromagnetism for odd numbers of holes, and its properties were investigated in detail. However, it was remained as a problem how we understand the complete alternation of magnetism between saturated ferromagnetism and singlet for odd and even numbers of holes, respectively. This alternation causes a difficulty when we consider the thermodynamic limit. In order to solve this difficulty, we investigate, at first, the change of the magnetization for systems with various boundary conditions, and we find that even for the even numbers of holes, the ground states are saturated ferromagnetic under the antiperiodic boundary condition. Furthermore, we explicitly investigate the spin-spin correlation functions < S z i S z j > to see the spin ordering. These calculations shows that all ground states in this filling region are the spiral state under a suitable boundary condition, and that the singlet states in these ground states, therefore, have a ferromagnetic order within, approximately, a half of the system size, although the total spin is still zero. From these results, we conclude that the properties in this region are by no means ill, and all ground states are essentially ferromagnetic in the sense that the spins in the singlet states are also ordered ferromagnetically if we take in the half of the system size.
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.
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The ground state of the two-dimensional Hubbard model on a square lattice is studied in the large-U limit in a half-filled band with a dynamical hole. For a 4\ifmmode\times\else\texttimes\fi{}4 lattice with hopping t=1 and coupling JJc{J}_{c}Jc​\ensuremath{\approxeq}0.075, the ground state has zero momentum (k) and spin 15/2 (ferromagnetic background). For J\ensuremath{\ge}Jc{J}_{c}Jc​ the ground state is degenerate with nonzero k and spin 1/2, in agreement with recent variational calculations. The nonzero k of the ground state comes from a nontrivial phase in the overlap of the spin states before and after a hole move. For small lattices we show that the effective Hamiltonian of the hole is that of a particle moving in a magnetic field. We also find that many of the features of the weak-coupling region carry over continuously to the strong-coupling region.