Quantum 2-Body Hamiltonian for Topological Color Codes

TL;DR

This paper presents a novel two-body quantum Hamiltonian on a 2D lattice that exhibits topological degeneracy and reproduces a topological color code, with unique features like strongly interacting anyonic excitations.

Contribution

Introduction of a two-body Hamiltonian model with topological degeneracy and a gapped phase mimicking a topological color code, featuring new non-perturbative effects and interactions.

Findings

Exact topological degeneracy in all coupling regimes

Presence of a gapped phase with topological color code properties

Three families of strongly interacting anyonic fermions

Abstract

We introduce a two-body quantum Hamiltonian model with spins-$\half$ located on the vertices of a 2D spatial lattice. The model exhibits an exact topological degeneracy in all coupling regimes. This is a remarkable non-perturbative effect. The model has a $\Z_2\times \Z_2$ gauge group symmetry and string-net integrals of motion. There exists a gapped phase in which the low-energy sector reproduces an effective topological color code model. High energy excitations fall into three families of anyonic fermions that turn out to be strongly interacting. All these, and more, are new features not present in honeycomb lattice models like Kitaev model.