Statistical translation invariance protects a topological insulator from interactions

TL;DR

This paper studies how statistical translation invariance can protect a two-dimensional topological insulator's edge modes from localization due to interactions and disorder, revealing a phase transition driven by interaction type.

Contribution

It demonstrates that statistical translation invariance prevents localization of Majorana edge modes under strong attractive interactions, a novel insight into topological insulator stability.

Findings

Majorana edge modes remain delocalized with strong attractive interactions

Repulsive interactions induce a transition to a localized phase

Self-duality symmetry explains the absence of localization under certain conditions

Abstract

We investigate the effect of interactions on the stability of a disordered, two-dimensional topological insulator realized as an array of nanowires or chains of magnetic atoms on a superconducting substrate. The Majorana zero-energy modes present at the ends of the wires overlap, forming a dispersive edge mode with thermal conductance determined by the central charge $c$ of the low-energy effective field theory of the edge. We show numerically that, in the presence of disorder, the $c=1/2$ Majorana edge mode remains delocalized up to extremely strong attractive interactions, while repulsive interactions drive a transition to a $c=3/2$ edge phase localized by disorder. The absence of localization for strong attractive interactions is explained by a self-duality symmetry of the statistical ensemble of disorder configurations and of the edge interactions, originating from translation invariance on the length scale of the underlying mesoscopic array.