Beyond Fermi-Liquid Theory: the $k$-Fermi liquids

TL;DR

This paper introduces the concept of $k$-Fermi liquids, a general framework for many-body fermion systems based on momentum as a good quantum number, unifying various known phenomena like Fermi liquids and Luttinger liquids.

Contribution

It proposes the $k$-Fermi liquid framework, demonstrating how it encompasses Fermi liquids, Luttinger liquids, and spin-charge separation, with two exactly solvable models as examples.

Findings

Unifies different fermionic systems under the $k$-Fermi liquid framework.

Shows how Fermi liquid, Luttinger liquid, and spin-charge separation emerge from this approach.

Provides two exactly solvable models illustrating the concepts.

Abstract

We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable $k$-Fermi liquid models with spin-charge separation are discussed as examples.