LeRoy Apker Award Talk: Anyons in a Dynamical Toric Code Model

In 3+1 dimensions, all particles are classified as either bosons or fermions. However the story is different in 2+1 dimensions, where a new type of particle exists: anyons. Beyond the fundamental interest of anyons, they also harness the ability to implement fault-tolerant universal quantum computation. The use of anyons for the purposes of quantum computation was first proposed by Kitaev with the development of the toric code model. However, the anyons in this model are stationary states, and the dynamics of anyons are an essential ingredient in quantum computation. In this work, we introduce a dynamical toric code model by perturbing the toric code Hamiltonian. Anyons in this model have non-trivial dynamics while the anyon numbers are conserved. In this talk I will discuss the model, the dispersion relation of the low energy excitations, and the role symmetry plays in the features of the spectrum.