Fourth Order Perturbation Theory for Normal Selfenergy in Repulsive Hubbard Model

TL;DR

This paper uses fourth order perturbation theory to more accurately evaluate the mass enhancement factor in the Hubbard model near half-filling, revealing significant effects from higher order diagrams on quasiparticle properties.

Contribution

It introduces a fourth order perturbative calculation of the selfenergy in the Hubbard model, providing a more precise estimate of mass enhancement effects near half-filling.

Findings

Large mass enhancement on the Fermi surface due to fourth order diagrams.

Mass enhancement increases with on-site repulsion U and density of states at the Fermi level.

Higher order effects influence the balance between superconducting transition temperature T_c and quasiparticle energy scales.

Abstract

We investigate the normal selfenergy and the mass enhancement factor in the Hubbard model on the two-dimensional square lattice. Our purpose in this paper is to evaluate the mass enhancement factor more quantitatively than the conventional third order perturbation theory. We calculate it by expanding perturbatively up to the fourth order with respect to the on-site repulsion $U$. We consider the cases that the system is near the half-filling, which are similar situations to high-$T_c$ cuprates. As results of the calculations, we obtain the large mass enhancement on the Fermi surface by introducing the fourth order terms. This is mainly originated from the fourth order particle-hole and particle-particle diagrams. Although the other fourth order terms have effect of reducing the effective mass, this effect does not cancel out the former mass enhancement completely and there remains still a large mass enhancement effect. In addition, we find that the mass enhancement factor becomes large with increasing the on-site repulsion $U$ and the density of state (DOS) at the Fermi energy $\rho(0)$. According to many current reseaches, such large $U$ and $\rho(0)$ enhance the effective interaction between quasiparticles, therefore the superconducting transition temperature $T_c$ increases. On the other hand, the large mass enhancement leads the reduction of the energy scale of quasiparticles, as a result, $T_c$ is reduced. When we discuss $T_c$, we have to estimate these two competitive effects.