Fourth-Order Perturbation Expansion for Hubbard Model on a Two-Dimensional Square Lattice

TL;DR

This paper applies fourth-order perturbation theory to the 2D Hubbard model, demonstrating good convergence and revealing detailed spectral features like Hubbard bands and pseudogaps, advancing understanding of strong correlation effects.

Contribution

It extends perturbation expansion to fourth order for the 2D Hubbard model, analyzing convergence and spectral properties in both half-filled and doped cases.

Findings

Perturbation series converges well for T > 0.1t in half-filled case.

Hubbard bands appear at ±U/2 with a pseudogap at the Fermi level.

Heavy quasiparticles form in doped cases at the Fermi level.

Abstract

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.