Landau-Fermi liquid analysis of the 2D t-t' Hubbard model

TL;DR

This paper uses perturbation theory to analyze the Landau interaction function in the 2D t-t' Hubbard model, exploring how interactions influence susceptibilities and Fermi surface properties within the Fermi liquid framework.

Contribution

It provides a detailed Landau-Fermi liquid analysis of the 2D t-t' Hubbard model, emphasizing the role of umklapp processes in Fermi surface anisotropy.

Findings

Elastic umklapp processes reduce compressibility anisotropically.

Spin and charge susceptibilities depend on interaction strength and band filling.

Higher order perturbation theory refines the understanding of Fermi liquid behavior.

Abstract

We calculate the Landau interaction function f(k,k') for the two-dimensional t-t' Hubbard model on the square lattice using second and higher order perturbation theory. Within the Landau-Fermi liquid framework we discuss the behavior of spin and charge susceptibilities as function of the onsite interaction and band filling. In particular we analyze the role of elastic umklapp processes as driving force for the anisotropic reduction of the compressibility on parts of the Fermi surface.