Quasipartice Spectra in the Hubbard Model

TL;DR

This paper investigates quasiparticle properties in the 2D Hubbard model using FLEX approximation, revealing how nesting, Van Hove singularities, and antiferromagnetic correlations influence scattering rates and spectral functions.

Contribution

It provides a detailed analysis of quasiparticle spectra considering next-nearest neighbor hopping and identifies the roles of Van Hove singularities and antiferromagnetic fluctuations.

Findings

Enhanced scattering along the Brillouin zone diagonal near half-filling.

Linear temperature dependence of scattering rate away from antiferromagnetic order.

Association of hot-spots with antiferromagnetic phase transition.

Abstract

We examine the quasiparticle lifetime and spectral weight near the Fermi surface in the two-dimensional Hubbard model. We use the FLEX approximation to self-consistently generate the Matsubara Green's functions and then we analytically continue to the real axis to obtain the quasiparticle spectral functions. We compare the spectral functions found in the nearest neighbor hopping only Hubbard model with those found when second neighbor hopping is included. This separates the effects of nesting, the Van Hove singularity and the short-ranged antiferromagnetic correlations. The quasiparticle scattering rate is enhanced along the (0,pi) to (pi,pi) Brillouin zone diagonal. When the density is close to half-filling these 'hot-spots' lie on the Fermi surface and the scattering rate increases with decreasing temperature. For the next-nearest neighbor hopping scenario we observe a large range of doping where there is no antiferromagnetism but the scattering rate has a linear temperature dependence. On decreasing the interaction this non-Fermi liquid behavior is confined to doping levels where the Fermi energy lies near to the Van Hove singularity. We conclude that the 'hot-spots' are associated with the antiferromagnetic phase transition while the linear temperature dependence of the scattering rate is associated with the Van Hove singularity.