Nonperturbative phase diagram of interacting disordered Majorana nanowires

TL;DR

This paper presents a nonperturbative analysis of a disordered Majorana nanowire, revealing a phase diagram with a topological superconducting phase and a localized glassy phase, using a Gaussian variational approach in replica space.

Contribution

It introduces a Gaussian variational method in replica space to study the phase diagram of disordered Majorana nanowires in the strong coupling regime, capturing non-perturbative effects.

Findings

Identifies two stable phases: topological superconducting and glassy localized phase.

Demonstrates the method's ability to handle strong disorder and interactions.

Reveals replica symmetry breaking in the localized phase.

Abstract

We develop a Gaussian variational approach in replica space to investigate the phase diagram of a one-dimensional interacting disordered topological superconducting wire in the strong coupling regime. This method allows for a non-perturbative treatment in the disorder strength, electron- electron interactions and the superconducting pairing amplitude. We find only two stable phases: a topological superconducting phase, and a glassy, non-topological localized phase, characterized by replica symmetry breaking.