Simple Exactly Solvable Models of non-Fermi Liquids

TL;DR

This paper introduces exactly solvable models in two dimensions that exhibit non-Fermi liquid behavior, characterized by highly degenerate ground states, absence of a Fermi surface, and non-analytic Green's functions, extending previous models.

Contribution

It generalizes the Hatsugai-Kohmoto model to higher dimensions, providing simple, exactly solvable non-Fermi liquid models with explicit ground states.

Findings

Ground states are highly degenerate.

No Fermi surface present in the models.

Green's functions exhibit branch cuts.

Abstract

We generalize the model of Hatsugai and Kohmoto [J. Phys. Soc. Jpn, 61, 2056 (1992)] and find ground states which do not show the properties of Fermi liquids. We work in two space dimensions, but it is straightforward to generalize to higher dimensions. The ground state is highly degenerate and there is no discontinuity in the momentum distribution; i.e., there is no Fermi surface. The Green's function generically has a branch cut.