Coulomb Interaction and the Fermi Liquid State: Solution by Bosonization

TL;DR

This paper uses bosonization to analyze the impact of Coulomb interactions on Fermi liquids, demonstrating that the Fermi liquid state persists under Coulomb forces, with specific behaviors for charge and spin excitations.

Contribution

It provides an exact bosonization analysis showing Coulomb interactions do not destroy the Fermi liquid state, clarifying the conditions under which non-Fermi liquid behavior arises.

Findings

Fermi liquid state is retained with Coulomb interactions

Spin and charge propagate together at the same velocity

Collective charge excitations exhibit an energy gap in three dimensions

Abstract

We investigate the effects of the Coulomb two-body interaction on Fermi liquids via bosonization. The Coulomb interaction is singular in the limit of low momentum transfer, and recent interest in the possibility that some singular interactions might destroy the Fermi liquid state motivate us to reexamine it. We calculate the exact boson correlation function to show that the Fermi liquid state is retained in the case of Coulomb interactions. Spin and charge degrees of freedom propagate together at the same velocity and collective charge excitations (plasmons) exhibit the expected energy gap in three dimensions. Non-Fermi liquid behavior occurs, however, for a super long range interaction studied recently by Bares and Wen.