A dynamical Toric Code model with fusion and de-fusion

TL;DR

This paper introduces a perturbed Toric Code model with dynamic anyonic excitations, revealing bound states, scattering states, and a transition between them, including Majorana fermions with Dirac cone dispersion.

Contribution

It presents a new two-parameter family of perturbations of the Toric Code with dynamic anyons, including bound states and scattering states, and analyzes their properties.

Findings

Existence of bound states and scattering states in the model.

Majorana fermions with Dirac cone dispersion.

Transition from bound to scattering states at a critical momentum.

Abstract

We introduce a two-parameter family of perturbations of Kitaev's Toric Code Model in which the anyonic excitations acquire an interesting dynamics. We study the dynamics of this model in the space of states with electric and magnetic charge both equal to 1 and find that the model exhibits both bound states and scattering states in a suitable region of the parameters. The bound state is a Majorana fermion with a dispersion relation of Dirac cone type. For a certain range of model parameters, we find that these bound states disappear in a continuum of scattering states at a critical value of the total momentum. The scattering states describe separate electric and magnetic anyons, which in this model each have a sin k dispersion relation.