Criteria and analytical results for the Pseudogap at the Van Hove point in two dimensions

TL;DR

This paper derives criteria and analytical results for the pseudogap at the Van Hove point in two-dimensional systems, revealing a shorter characteristic length scale and abnormal single-particle properties, with validation against Monte Carlo simulations.

Contribution

It introduces a new criterion for the pseudogap at the Van Hove point and provides analytical results applicable in both frequency representations, validated by numerical simulations.

Findings

Characteristic length scale at Van Hove point is proportional to 1/T^{1/2}

Identifies regime with abnormal single-particle properties

Analytical results match Monte Carlo simulations

Abstract

I establish the criteria and obtained analytical results for the pseudogap at the Van Hove (antinodal) point on the Fermi surface in two dimensions. The original criterion $\xi >> \xi_{th\_db}=v_F/\pi T$ is not applicable in this case since Fermi velocity $v_F=0$. It turns out that the characteristic length for the pseudogap crossover at the Van Hove point $\xi_{th\_vh} \propto 1/T^{1/2}$, which is significantly shorter than the one at the regular Fermi surface points $\xi_{th\_db} \propto 1/T$. In particular, $\xi_{th\_vh}$ is between one and two lattice spacing in the intermediate interaction regime of the Hubbard model. I have also identified the regime where there is still a single maximum in the spectral function, but single particle properties are abnormal. Specifically, the imaginary part of the self-energy has a minimum instead of maximum at the Fermi level and the slope of the real part of the self-energy is positive instead of negative. The important advantages of an analytical approach is that it provides results in both the Matsubara frequency representation and in real frequencies representation. I compare Matsubara frequency results with the exact numerical results of the Monte Carlo methods in the Hubbard model and then show what they correspond to in the real frequency self-energy and spectral function.