Anisotropic pseudogap in the half-filling 2-d Hubbard model at finite T

TL;DR

This study investigates the formation of an anisotropic pseudogap in the half-filling 2D Hubbard model at finite temperature, revealing its origin from spin fluctuations and Fermi surface nesting in the weak-coupling regime.

Contribution

The paper introduces a theoretical framework using Green's functions with one-loop self-energy corrections to explain pseudogap formation and its momentum dependence in the 2D Hubbard model.

Findings

Pseudogap appears in the density of states and spectral function at the Fermi level.

The pseudogap's anisotropy is linked to spin fluctuations and band structure features.

Theoretical conditions for pseudogap formation are established through two proven theorems.

Abstract

We have studied the pseudogap formation in the single-particle spectra of the half-filling two-dimensional Hubbard model. Using a Green's function with the one-loop self-energy correction of the spin and charge fluctuations, we have numerically calculated the self-energy, the spectral function, and the density of states in the weak-coupling regime at finite temperature. Pseudogap formations have been observed in both the density of states and the spectral function at the Fermi level. The pseudogap in the spectral function is explained by the non-Fermi-liquid-like nature of the self-energy. The anomalous behavior in the self-energy is caused by both the strong antiferromagnetic spin fluctuation and the nesting condition on the non-interacting Fermi surface. In the present approximation, we find a logarithmic singularity in the integrand of the imaginary part of the self-energy. Concerning the energy dependence of the spectral function and the self-energy, two theorems are proved. They give a necessary condition in the self-energy to produce the pseudogap at the Fermi level. The pseudogap in the spectral function is highly momentum dependent on the Fermi surface. It opens initially in the $(\pm \pi,0)$, $(0,\pm \pi)$ regions as the normal state pseudogap observed in the high-$T_c$ superconductors and if the interaction is increased, it spreads to other Fermi surface sectors. The anisotropy of the pseudogap is produced by the low-energy enhancement of the spin excitation around ${\bf Q}=(\pi,\pi)$ and the flatness of the band dispersion around the saddle point.