Fermion condensation in a generalized Hatsugai-Kohmoto model with momentum-mixing Landau interactions

TL;DR

This paper extends the exactly solvable Hatsugai-Kohmoto model by adding momentum-mixing Landau interactions, revealing a fermion condensation scenario with a partially flat band and mapping to a generalized Ising model.

Contribution

It introduces momentum-mixing Landau interactions into the HK model and provides a self-consistent mean-field analysis and an exactly solvable variant.

Findings

Ground state exhibits a partially flat energy band.

Model maps onto a generalized Ising model with two spins per reciprocal lattice site.

Proposes an exactly solvable model with a unique ground state for all densities.

Abstract

The Hatsugai-Kohmoto (HK) model is an exactly solvable electronic lattice model where the interaction between electrons with opposite spin is diagonal in momentum space. We generalize the HK model by introducing momentum-mixing Landau interactions. Within a self-consistent mean-field analysis we find that the ground state of this model exhibits a partially flat energy band, in agreement with the fermion condensation scenario proposed by Khodel and Shaginyan [JETP Lett. 51, 553 (1990)]. Inspired by Andersons pseudospin formulation of BCS theory, we show that the HK model with Landau interactions can be mapped onto a generalized Ising model where each site of the reciprocal lattice hosts two Ising spins. In the pseudospin picture the emergence of a partially flat electronic band corresponds to the smoothing of a magnetic domain wall. Moreover, guided by the pseudospin picture, we propose an exactly solvable variant of the HK model which has a unique ground state for all densities.