Fourth-Order Perturbation Expansion for Hubbard Model on a Two-Dimensional Square Lattice(Condensed matter: electronic structure and electrical, magnetic, and optical properties)

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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 ω≃±U/2, and a pseudogap appears at the Fermi level ω=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.
社団法人日本物理学会の論文
2008-06-15