Fibonacci Topological Superconductor

In this talk we will present 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/(G₂)₁ coset factorization, leads to a solvable one dimensional model without parafermions that is extended to two dimensions using a network construction. In addition, we predict a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We will show that Majorana fermions can split into a pair of Fibonacci anyons, and propose an interferometer that generalizes the Z₂ Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.