Fibonacci Topological Superconductor

TL;DR

This paper introduces a solvable model of interacting Majorana fermions that realizes a Fibonacci topological superconductor, predicting a new phase with Fibonacci anyons and proposing an interferometer to detect their non-Abelian statistics.

Contribution

It presents a novel theoretical model for a Fibonacci topological superconductor based on a coset construction, without relying on parafermions, and extends it to two dimensions.

Findings

Predicts a Fibonacci topological phase with non-Abelian anyons.

Proposes an interferometer to detect Fibonacci anyon statistics.

Introduces an anti-Fibonacci phase related to the tricritical Ising model.

Abstract

We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a $SO(7)_1/(G_2)_1$ coset factorization, leads to a solvable one dimensional model that is extended to two dimensions using a network construction. In addition to providing a description of the Fibonacci phase without parafermions, our theory predicts a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We show that Majorana fermions can split into a pair of Fibonacci anyons, and propose an interferometer that generalizes the $Z_2$ Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.