Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion

TL;DR

This paper presents a method to identify and analyze Majorana modes in interacting quantum systems using local integrals of motion, extending understanding of topological protection in complex many-body environments.

Contribution

It introduces a novel approach to construct and study Majorana fermions in interacting systems, including effects of interactions on their properties and stability.

Findings

Method reproduces known results in non-interacting models

Interactions affect the spatial structure of Majorana modes

Long-term information retention depends on topological protection

Abstract

Recently, there has been substantial progress in methods of identifying local integrals of motion in interacting integrable models or in systems with many-body localization. We show that one of these approaches can be utilized for constructing local, conserved, Majorana fermions in systems with an arbitrary many-body interaction. As a test case, we first investigate a non-interacting Kitaev model and demonstrate that this approach perfectly reproduces the standard results. Then, we discuss how the many-body interactions influence the spatial structure and the lifetime of the Majorana modes. Finally, we determine the regime for which the information stored in the Majorana correlators is also retained for arbitrarily long times at high temperatures. We show that it is included in the regime with topologically protected soft Majorana modes, but in some cases is significantly smaller.