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Journal of the Physical Society of Japan

Perturbation Calculation ofk-Mass for Two-Dimensional Hubbard Model with Long-Range Coulomb Interaction

Shuntaro Yoda, Kōsaku Yamada

Published May 15, 1998• 2 citations
Publisher

Abstract

We investigate the two-dimensional Hubbard model with the long-range Coulomb interaction. We assume the form of the effective Coulomb interaction, which is treated as a perturbation. For the half-filling case, the self-energy is numerically evaluated up to the second-order terms of the perturbation expansion with the full momentum dependence included. The k -mass is calculated from this self-energy. It is found that the first-order term makes a dominant contribution to the reduction of the k -mass.

DOI
10.1143/jpsj.67.1682

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We investigate the two-dimensional Hubbard model with the long-range Coulomb interaction. We assume the form of the effective Coulomb interaction, which is treated as a perturbation. For the half-filling case, the self-energy is numerically evaluated up to the second-order terms of the perturbation expansion with the full momentum dependence included. The k -mass is calculated from this self-energy. It is found that the first-order term makes a dominant contribution to the reduction of the k -mass.
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We investigate the Hubbard model on a two-dimensional square lattice by the perturbation expansion to the fourth order in the on-site Coulomb repulsion U. Numerically calculating all diagrams up to the fourth order in self-energy, we examine the convergence of perturbation series in the lattice system. We indicate that the coefficient of each order term rapidly decreases as in the impurity Anderson model for T > 0.1t in the half-filled case, but it holds in the doped case even at lower temperatures. Thus, we can expect that the convergence of perturbation expansion in U is very good in a wide parameter region also in the lattice system, except for T < 0.1t in the half-filled case. We next calculate the density of states in the fourth-order perturbation. In the half-filled case, the shape in a moderate correlation regime is quite different from the three peak structure in the second-order perturbation. Remarkable upper and lower Hubbard bands locate at w = +(-)U/2, and a pseudogap appears at the Fermi level w=0. This is considered as the precursor of the Mott-Hubbard antiferromagnetic structure. In the doped case, quasiparticles with very heavy mass are formed at the Fermi level. Thus, we conclude that the fourth-order perturbation theory overall well explain the asymptotic behaviors in a strong correlation regime.
In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4{ital t} of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended {ital s}- and {ital d}-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the {ital d}-wave correlation function, that is, {ital d}-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.
In the first part of this paper we explore a configuration-interaction approach to the two-dimensional Hubbard model near half filling. To reproduce the result of degenerate second-order perturbation theory it is necessary to include Fock states having kinetic energy within 4t of the lowest kinetic-energy states. Using the ground state from the largest configuration-interaction calculation, we calculate the extended s- and d-wave superconducting correlation functions as a function of distance. There are indications of a nondecaying long-distance tail in the d-wave correlation function, that is, d-wave superconductivity in the ground state of the repulsive Hubbard model. In the second part of the paper, we reexamine our effective Hamiltonian for the repulsive Hubbard model near half filling. Simple considerations lead us to a more intuitively plausible form consistent with our previous results and spin-rotational invariance.
We apply self-consistent second order perturbation theory (SCSOPT) with respect to the on-site repulsive interaction U to study the Hubbard model in two dimensions. We investigate single particle properties of the model over the entire doping range at zero temperature. It is shown that as doping decreases toward half-filling ωωω-mass enhancement factor increases, while k-mass enhancement factor decreases. The increase in ωωω-mass enhancement factor is larger than the decrease in k-mass enhancement factor, so that total-mass is larger than that in the non-interacting case. When particle number density per unit cell n is given by 0.64