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arXiv:cond-mat/9703022

Low density ferromagnetism in Extended Hubbard ( t-t'-U ) Model

P. A. Sreeram, Suresh G. Mishra

Published Mar 3, 1997• 0 citations
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Abstract

We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for $$, the particle density with spin $σ$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor hopping element t' when on-site interaction U is large. The phase diagram as a function of t'/t and the electron density $$ has been obtained by numerically solving the self consistent equation. It is found that the maximum density at which ferromagnetism can occur, peaks around $t'/t \approx -0.53$. We show that this phenomenon is a result of the peculiar way in which the t' term modifies the density of states.

DOI
10.48550/arxiv.cond-mat/9703022

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We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for , the particle density with spin $σ$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor hopping element t' when on-site interaction U is large. The phase diagram as a function of t'/t and the electron density has been obtained by numerically solving the self consistent equation. It is found that the maximum density at which ferromagnetism can occur, peaks around t′/t≈−0.53t'/t \approx -0.53t′/t≈−0.53. We show that this phenomenon is a result of the peculiar way in which the t' term modifies the density of states.
Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest-neighbor hopping amplitude t1 tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the t1—U plane.
We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2{t}_{2}t2​) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t2{t}_{2}t2​\ensuremath{\ne}0. We study the behavior of spin-spin correlation functions for small lattices of up to N=64 atoms using Monte Carlo simulations, as well as exact diagonalization for N=4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the half-filled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.
Using exact diagonalization techniques, the Hubbard model with hopping between nearest (t) and next-nearest neighbors ${(t}^{\ensuremath{'}})$ is studied in a two-dimensional cluster with $4\ifmmode\times\else\texttimes\fi{}4$ sites. Within a range of values of ${t}^{\ensuremath{'}}<0$ and low densities, states with different total spin are degenerate in the noninteracting system. At a finite value of the Coulomb repulsion U, states with high spin are energetically favored and the ground state can be fully polarized. The behavior of the density of states differs from that obtained within the Hartree-Fock approximation. The low energy region of the density of states (DOS) for the majority spins remains weakly modified by U. Our results bring further support to the idea that itinerant ferromagnetism occurs in strongly correlated systems with high noninteracting DOS at the bottom of the band.
Using an improved version of the projection quantum Monte Carlo technique, we study the square-lattice Hubbard model with nearest-neighbor hopping ttt and next-nearest-neighbor hopping ${t}^{\ensuremath{'}}$ by simulation of lattices with up to $20\ifmmode\times\else\texttimes\fi{}20$ sites. For a given ${R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2t}^{\ensuremath{'}}/t$, we consider that filling which leads to a singular density of states of the noninteracting problem. For repulsive interactions, we find an itinerant ferromagnet (antiferromagnet) for R=0.94R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.94R=0.94 ( R=0.2R\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2R=0.2). This is consistent with the prediction of the TTT-matrix approximation, which sums the most singular set of diagrams.
We examined a one-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping with up to 32 sites by means of the density-matrix renormalization-group method. The model has two energy bands and includes the flat-band model studied by Tasaki as a special case. The model with finite band dispersion is found to show metallic (saturated) ferromagnetism for a sufficiently strong interaction. No partially polarized ground state is found. The interaction necessary to realize a ferromagnetic ground state becomes weak when the electron density is decreased from the quarter-filling.
A single-band Hubbard model with nearest and next-nearest neighbor hopping is studied for d=1, 2, 3, using both analytical and numerical techniques. In one dimension, saturated ferromagnetism is found above a critical value of U for a band structure with two minima and for small and intermediate densities. This is an extension of a scenario recently proposed by M\"uller-Hartmann. For three dimensions and nonpathological band structures, it is proven that such a scenario does not work. \textcopyright{} 1996 The American Physical Society.