End-to-end correlations in the Kitaev chain

TL;DR

This paper investigates how end-to-end correlations in the Kitaev chain relate to topological phases and Majorana fermions, providing an analytical expression linking correlations to topological signatures.

Contribution

It introduces a method to analyze correlations in the Kitaev chain and derives a simple analytical expression connecting correlations with topological phases.

Findings

End-to-end correlations indicate topological phases.

Classical correlations serve as signatures of Majorana fermions.

Analytical expression links correlations to topological properties.

Abstract

The interdependence between long range correlations and topological signatures in fermionic arrays is examined. End-to-end correlations, in particular classical correlations, maintain a characteristic pattern in the presence of delocalized excitations and this behavior can be used as an operational criterion to identify Majorana fermions in one-dimensional systems. The study discusses how to obtain the chain eigenstates in tensor-state representation together with the proposed assessment of correlations. Outstandingly, the final result can be written as a simple analytical expression that underlines the link with the system's topological phases.