A many-body interpretation of Majorana bound states, and conditions for their localisation

TL;DR

This paper establishes a general condition for the existence and localization of Majorana bound states in many-body systems, linking their properties to ground state degeneracy protection and validating results through applications to non-interacting and interacting models.

Contribution

It introduces a new many-body framework to determine Majorana state localization, extending previous single-particle analyses to interacting systems.

Findings

Derived a general localization condition for Majorana states

Confirmed exponential decay in the Kitaev chain matches many-body and single-particle results

Applied the framework to interacting systems with evidence of Majorana states

Abstract

We derive a condition for the existence of completely or exponentially localised Majorana bound states (with the potential for non-Abelian statistics) in a generic many-body system. We discuss the relationship between the existence of these operators and the protection of the ground state degeneracy from local perturbations. We use our methods to study the exponential decay of the Majorana bound states in the non-interacting Kitaev chain, finding complete agreement between our many-body calculation and single-particle results. We then apply these results to various interacting systems which have previous evidence for Majorana bound states.