# Partially gapped fermions in 2D - Mathematical Physics

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Abstract: We compute mean field phase diagrams of two closely related interactingfermion models in two spatial dimensions 2D. The first is the so-called 2Dt-t-V model describing spinless fermions on a square lattice with localhopping and density-density interactions. The second is the so-called 2DLuttinger model that provides an effective description of the 2D t-t-V modeland in which parts of the fermion degrees of freedom are treated exactly bybosonization. In mean field theory, both models have a charge-density-waveCDW instability making them gapped at half-filling. The 2D t-t-V model has asignificant parameter regime away from half-filling where neither the CDW northe normal state are thermodynamically stable. We show that the 2D Luttingermodel allows to obtain more detailed information about this mixed region. Inparticular, we find in the 2D Luttinger model a partially gapped phase that, aswe argue, can be described by an exactly solvable model.

Author: ** Jonas de Woul, Edwin Langmann**

Source: https://arxiv.org/