Interacting Electrons on a Square Fermi Surface

TL;DR

This paper maps interacting electrons on a square Fermi surface onto quantum chains, revealing non-Fermi liquid behavior, spin-charge separation, and insulating states at half-filling, providing a new analytical approach.

Contribution

It introduces a novel mapping technique for analyzing electron interactions on a square Fermi surface, enabling exact solutions and insights into non-Fermi liquid states.

Findings

Fermi liquid behavior is destroyed by interactions.

Square Fermi surface remains stable under doping.

Half-filling leads to a charge gap and insulating behavior.

Abstract

Electronic states near a square Fermi surface are mapped onto quantum chains. Using boson-fermion duality on the chains, the bosonic part of the interaction is isolated and diagonalized. These interactions destroy Fermi liquid behavior. Non-boson interactions are also generated by this mapping, and give rise to a new perturbation theory about the boson problem. A case with strong repulsions between parallel faces is studied and solved. There is spin-charge separation and the square Fermi surface remains square under doping. At half-filling, there is a charge gap and insulating behavior together with gapless spin excitations. This mapping appears to be a general tool for understanding the properties of interacting electrons on a square Fermi surface.