Journal of the Physical Society of Japan

Langevin Simulation of the Two-Dimensional Hubbard Model

Kazuo Saitoh, Satoshi Takada

Published Mar 15, 1989• 6 citations

Abstract

The two-dimensional (2-D) Hubbard model with nearest-neighbor and next-nearest-neighbor (n.n.n.) hopping are studied using the Langevin method. Results of the staggered magnetic susceptibility and the pairing susceptibilities are shown. It is found that the effect of n.n.n. hopping destroys the antiferromagnetic correlation and assists the tendency of pairing. The possibility of superconductivity in the Hubbard model in the presence of n.n.n. hopping is discussed.

DOI: 10.1143/jpsj.58.783

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Journal of the Physical Society of Japan

Langevin Simulation of the Two-Dimensional Hubbard Model

Kazuo Saitoh, Satoshi Takada

Published Mar 15, 1989• 6 citations

Publisher

Abstract

DOI: 10.1143/jpsj.58.783

Related papers

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We study the behavior of pair susceptibilities in the two-dimensional repulsive Hubbard model with next-nearest-neighbor hopping

{t}_{2}

by Monte Carlo simulations. In a certain range of band filling, we find that the d-wave pair susceptibilities can be enhanced by a Hubbard repulsion U with respect to the noninteracting case, unlike the case with

{t}_{2}

=0. We discuss the connection of this model to

{\mathrm{CuO}}_{2}

planes in the oxide superconductors and the possible implication of our results for these materials.

We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (

{t}_{2}

) 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

{t}_{2}

\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.