Exactly solvable chain of interacting electrons with correlated hopping and pairing

Abstract

A generalization of the Mattic-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 one-site Hubbard interaction U and the correlated hopping and pairing t. The ground-state phase diagram of the model is calculated in the coordinates t − U , the region of existence of topological states is determined. It is shown that low-energy excitations destroy bonds between fermions in the chain, leading to a dielectric state.

Mott transition in two-band fermion model with on-site Coulomb repulsion

“…The experimental discovery of the first Weyl semimetal in TaAs 1 gave impetus to the study of topological gapless states in real compounds. The topological features of the phase state determine the chiral surface states: in one-dimensional systems, these are the zero energy Majorana states 2,3 (the Majorana fermions), in two-dimensional systems, they are chiral edge modes localized at the boundaries 4,5 (the Dirac fermions), in three-dimensional systems they are the Weyl nodes and topological surface states 1,6,7 (the Weyl fermions). As a rule, topological surface states of fermions exist for a certain dimension of the system.…”