Exactly solvable chain of interacting electrons with correlated hopping and pairing

Highlights: • The exact solution of 1D models of electrons interacting via on-site Hubbard repulsion and correlated hopping and pairing is obtained. • Criterion for realizing the topological state is calculated. • The ground-state phase diagram is calculated. -- Abstract: A generalization of the Mattis-Nam model Mattis and Nam (1972) [7], 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.