Partially gapped fermions in 2D

TL;DR

This paper analyzes phase diagrams of 2D interacting fermion models, revealing a partially gapped phase in the 2D Luttinger model that extends understanding of fermionic behavior beyond half-filling.

Contribution

It introduces a detailed mean field analysis of two related 2D fermion models and uncovers a novel partially gapped phase in the 2D Luttinger model.

Findings

Both models exhibit charge-density-wave instability at half-filling.

The 2D Luttinger model reveals a partially gapped phase away from half-filling.

The partially gapped phase can be described by an exactly solvable model.

Abstract

We compute mean field phase diagrams of two closely related interacting fermion models in two spatial dimensions (2D). The first is the so-called 2D t-t'-V model describing spinless fermions on a square lattice with local hopping and density-density interactions. The second is the so-called 2D Luttinger model that provides an effective description of the 2D t-t'-V model and in which parts of the fermion degrees of freedom are treated exactly by bosonization. In mean field theory, both models have a charge-density-wave (CDW) instability making them gapped at half-filling. The 2D t-t'-V model has a significant parameter regime away from half-filling where neither the CDW nor the normal state are thermodynamically stable. We show that the 2D Luttinger model allows to obtain more detailed information about this mixed region. In particular, we find in the 2D Luttinger model a partially gapped phase that, as we argue, can be described by an exactly solvable model.