Study of a toy model and its relation to the Hubbard model with infinite range hopping

TL;DR

This paper investigates a toy model of strongly correlated fermions, revealing a metal-insulator transition and establishing its equivalence to the Hubbard model with infinite range hopping, including generalizations to multiple components.

Contribution

It introduces a simplified fermion model and demonstrates its equivalence to an infinite-range Hubbard model, extending the analysis to N-component systems.

Findings

Identifies a metal-insulator transition in the toy model.

Establishes equivalence with the Hubbard model with infinite range hopping.

Generalizes the model to N components.

Abstract

A toy model of strongly correlated fermions is studied using Green function and functional integration methods. The model exhibits a metal-insulator transition as the interaction is varied. In the case of unrestricted hopping is established the equivalence of the model with the Hubbard model with infinite range hopping. The generalization to the case with $N$ components is made.