Electrical Conductivity of Fermi Liquids. I. Many-body Effect on the Drude Weight

TL;DR

This paper examines how many-body interactions influence the Drude weight in Fermi liquids, highlighting the role of Umklapp processes and the effective mass, with implications for lattice systems and electron density.

Contribution

It demonstrates that many-body effects modify the Drude weight via Umklapp processes and clarifies the distinction between effective mass and quasiparticle velocity in Fermi liquids.

Findings

Drude weight is affected by electron-electron interactions in lattice systems.

In Galilean invariant systems, the Drude weight remains unrenormalized.

Perturbation theory shows significant changes in Drude weight near half filling.

Abstract

On the basis of the Fermi liquid theory, we investigate the many-body effect on the Drude weight. In a lattice system, the Drude weight $D$ is modified by electron-electron interaction due to Umklapp processes, while it is not renormalized in a Galilean invariant system. This is explained by showing that the effective mass $m'$ for $D\propto n/m'$ is defined through the current, not velocity, of quasiparticle. It is shown that the inequality $D>0$ is required for the stability against the uniform shift of the Fermi surface. The result of perturbation theory applied for the Hubbard model indicates that $D$ as a function of the density $n$ is qualitatively modified around half filling $n\sim 1$ by Umklapp processes.