# Exactly solvable chain of interacting electrons with correlated hopping and pairing

## TL;DR

This paper introduces an exactly solvable model of interacting electrons with correlated hopping and pairing, analyzing topological states and the stability of Majorana fermions in a complex quantum chain.

## Contribution

It generalizes the Mattis-Nam model to include correlated hopping and pairing, providing an exact solution and exploring topological phases and Majorana fermion stability.

## Key findings

- Identified the phase diagram including topological states.
- Showed low-energy excitations can induce an insulating state.
- Analyzed stability of boundary Majorana fermions.

## Abstract

A generalization of the Mattis-Nam model (J.Math.Phys., 13 (1972), 1185), which takes into account a correlated hopping and pairing of electrons, is proposed, its exact solution is obtained. In the framework of the model the stability of the zero energy Majorana fermions localized at the boundaries is studied in the chain in which electrons interact through both the on-site Hubbard interaction and the correlated hopping and pairing. The ground-state phase diagram of the model is calculated, the region of existence of topological states is determined. It is shown that low-energy excitations destroy bonds between electrons in the chain, leading to an insulator state.