# Generalized Falicov-Kimball Models

## TL;DR

This paper extends the Falicov-Kimball model to include non-fermionic quasi-particles like Majorana fermions, exploring new theoretical models and their potential applications in superconductivity and spin systems.

## Contribution

It introduces generalized Falicov-Kimball models with Majorana fermions and spin-dependent hopping, expanding the theoretical framework of correlated electron systems.

## Key findings

- Developed extended MFKM with Majorana fermions
- Analyzed p-wave BCS superconductor on bipartite lattice
- Explored BCS-Anderson model with Majorana fermions

## Abstract

In this paper we extend the Falicov-Kimball model (FKM) to the case where the "quasi-particles" entering the FKM are not "ordinary" fermions. As an example we first discuss how the FKM can be generalized to the case with spin-dependent hopping. Afterwards we discuss several cases where the "quasi-particles" entering the FKM are Majorana fermions (extended Majorana-Falicov-Kimball Model (MFKM). Two examples of extended MFKM are discussed in detail: (i) a $p$-wave BCS superconductor on a bipartite lattice and (ii) a BCS-Anderson model. We also discuss the most general forms of extended MFKM, including a brief discussion on the case where the Majorana fermions represent spins, but not real fermion particles.