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Chinese Journal of Physics

Two-Dimensional Infinite U Hubbard Model Studied by the Power Lanczos Method

Y. C. Chen, C. T. Shih, T. K. Lee

Published Apr 1, 1996• 0 citations
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Abstract

Using the power-Lanczos method me study the ground state (GS) properties of the two-dimension infinite U Hubbard model (IUHM) for 8 x 8 and 10 x 10 square lattices. We found that the charge structure factor of IUHM is very similar to that of hard core boson (ZZB). By comparing the GS energies of IUHM and spinless fermion wedetermined the critical hole density 6, ~ 0.26 above which the Nagaoka state becomes unstable.

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•Jan 1, 1999•4 citations
Using the power-Lanczos method me study the ground state (GS) properties of the two-dimension infinite U Hubbard model (IUHM) for 8 x 8 and 10 x 10 square lattices. We found that the charge structure factor of IUHM is very similar to that of hard core boson (ZZB). By comparing the GS energies of IUHM and spinless fermion wedetermined the critical hole density 6, ~ 0.26 above which the Nagaoka state becomes unstable.
We use exact diagonalization in order to study the infinite-U limit of the two-dimensional Hubbard model. As well as looking at single-particle correlations, such as ${\mathit{n}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}$=〈${\mathit{c}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${\mathit{c}}_{\mathit{k}\mathrm{\ensuremath{\sigma}}}$〉, we also study N-particle correlation functions, which compare the relative positions of all the particles in different models. In particular we study 16- and 18-site clusters and compare the charge correlations in the Hubbard model with those of spinless fermions and hard-core bosons. We find that although low densities of holes favor a ``locally ferromagnetic'' fermionic description, the correlations at larger densities resemble those of pure hard-core bosons surprisingly well.
The infinite-U Hubbard model on finite two-dimensional square lattices is investigated by the use of exact numerical diagonalization. Configurations with one spin flip away from the ferromagnetic state and up to three holes are studied for lattice sizes ranging from 4*4 to 12*12. For all these situations, the state with one spin flip is found to be more stable than the Nagaoka ferromagnetic state. The crystal momentum of the ground state in this spin sector depends on the system size. Systematic comparison with the Gutzwiller wavefunction shows that it reproduces qualitatively the crystal momentum dependence of the energy, but not the exact correlation between the spin flip and the holes.
We present different numerical calculations based on variational quantum Monte Carlo simulations supporting a ferromagnetic ground state for finite and small hole densities in the two-dimensional infinite-U Hubbard model. Moreover, by studying the energies of different total spin sectors, these calculations strongly suggest that the paramagnetic phase is unstable against a phase with a partial polarization for large hole densities delta approximately 0.40 with evidence for a second-order transition to the paramagnetic large doping phase.
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