Localization-enhanced and degraded topological-order in interacting p-wave wires

TL;DR

This study investigates how disorder affects the stability and localization of many-body zero modes in interacting p-wave wires, revealing complex behaviors that depend on the system's parameters and challenging simple correlations with many-body localization.

Contribution

It provides a detailed numerical analysis of the interplay between disorder, interactions, and topological zero modes in a Kitaev chain, highlighting nuanced effects on localization and stability.

Findings

Disorder can both suppress and enhance zero mode localization depending on the regime.

Interaction-induced decay transitions are affected differently by disorder in different parameter regions.

Measures of many-body localization do not always correlate with zero mode stability.

Abstract

We numerically study the effect of disorder on the stability of the many body zero mode in a Kitaev chain with local interactions. Our numerical procedure allows us to resolve the position-space and multi-particle structure of the zero modes, as well as providing estimates for the mean energy splitting between pairs of states of opposite fermion parity, over the full many-body spectrum. We find that the parameter space of a clean system can be divided into regions where interaction induced decay transitions are suppressed (Region I) and where they are not (Region II). In Region I we observe that disorder has an adverse effect on the zero mode, which extends further into the bulk and is accompanied by an increased energy splitting between pairs of states of opposite parity. Conversely Region II sees a more intricate effect of disorder, showing an enhancement of localization at the system's end accompanied by a reduction in the mean pairwise energy splitting. We discuss our results in the context of the Many-Body Localization (MBL). We show that while the mechanism that drives the MBL transition also contributes to the fock-space localization of the many-body zero modes, measures that characterize the degree of MBL do not necessarily correlate with an enhancement of the zero-mode or an improved stability of the topological region.