Softening of Majorana edge states by long-range couplings

TL;DR

This paper investigates how long-range couplings in the Kitaev chain affect Majorana edge states, revealing they become more delocalized at a universal rate and altering the topological nature of the critical point.

Contribution

It demonstrates analytically how long-range interactions soften Majorana edge states and modify the topological index at criticality in the Kitaev chain.

Findings

Majorana states soften and delocalize with increasing interaction range

The topological index changes at criticality, indicating a shift in topological phase

The critical point resembles a trivial phase rather than an interpolating phase

Abstract

The inclusion of long-range couplings in the Kitaev chain is shown to modify the universal scaling of topological states close to the critical point. By means of the scattering approach, we prove that the Majorana states \textit{soften}, becoming increasingly delocalised at a universal rate which is only determined by the interaction range. This edge mechanism can be related to a change in the value of the bulk topological index at criticality, upon careful redefinition of the latter. The critical point turns out to be topologically akin to the trivial phase rather than interpolating between the two phases. Our treatment moreover showcases how various topological aspects of quantum models can be investigated analytically.