Fibonacci topological order from quantum nets

TL;DR

This paper introduces a quantum net model exhibiting non-abelian doubled Fibonacci topological order, with a Hamiltonian applicable to any lattice, featuring simplified interactions and dynamic excitations, supported by evidence of a spectral gap.

Contribution

It presents a new quantum net Hamiltonian that realizes doubled Fibonacci topological order with simplified interactions and dynamical excitations, expanding the understanding of topological phases.

Findings

The model exhibits non-abelian doubled Fibonacci topological order.

The Hamiltonian is defined on any lattice with less complex interactions.

Strong evidence of a spectral gap from exact diagonalization.

Abstract

We analyze a model of quantum nets and show it has non-abelian topological order of doubled Fibonacci type. The ground state has the same topological behavior as that of the corresponding string-net model, but our Hamiltonian can be defined on any lattice, has less complicated interactions, and its excitations are dynamical, not fixed. This Hamiltonian includes terms acting on the spins around a face, around a vertex, and special "Jones-Wenzl" terms that serve to couple long loops together. We provide strong evidence for a gap by exact diagonalization, completing the list of ingredients necessary for topological order.