Topological order from quantum loops and nets

TL;DR

This paper introduces quantum loop and net models exhibiting topological order and non-abelian anyons, with a self-dual Hamiltonian that is simple to implement, advancing understanding of topological phases.

Contribution

It presents a new class of quantum models with topological order, linking loop and net models through chromatic polynomial weights and deriving a simple, self-dual Hamiltonian.

Findings

Models support deconfined non-abelian anyons

Quantum self-duality simplifies Hamiltonian construction

Square lattice Hamiltonian involves only four-spin interactions

Abstract

I define models of quantum loops and nets which have ground states with topological order. These make possible excited states comprised of deconfined anyons with non-abelian braiding. With the appropriate inner product, these quantum loop models are equivalent to net models whose topological weight involves the chromatic polynomial. A useful consequence is that the models have a quantum self-duality, making it possible to find a simple Hamiltonian preserving the topological order. For the square lattice, this Hamiltonian has only four-spin interactions.