Effect of interaction on the Majorana zero modes in the Kitaev chain at half filling

TL;DR

This paper investigates how fermion-fermion interactions influence Majorana zero modes in a half-filled Kitaev chain, revealing a special interaction strength where zero modes are maximally localized and degenerate.

Contribution

It identifies a specific interaction value in the interacting Kitaev chain where Majorana zero modes are enhanced and degenerate, providing new insights into topological properties under interactions.

Findings

Zero-energy Majorana modes are maximally localized at a specific interaction U_p.

Ground states are strictly two-fold degenerate at U_p even for finite chain length.

Interaction U_p can be attractive or repulsive depending on system parameters.

Abstract

The one dimension interacting Kitaev chain at half filling is studied. The symmetry of the Hamiltonian is examined by dual transformations and various physical quantities as functions of the fermion-fermion interaction $U$ are calculated systematically using the density matrix renormalization group method. A special value of interaction $U_p$ is revealed in the topological region of the phase diagram. We show that at $U_p$ the ground states are strictly two-fold degenerate even though the chain length is finite and the zero-energy peak due to the Majorana zero modes is maximally enhanced and exactly localized at the end sites. $U_p$ may be attractive or repulsive depending on other system parameters. We also give a qualitative understanding of the effect of interaction under the self-consistent mean field framework.