Excitation basis for gauge models of topological phases (Dr. C. Delcamp)

By considering the gluing of excited states on tubes, we can reveal the mathematical structure of the excitations, namely the Drinfel’d double. In three dimensions, the same Hamiltonian yields excitations located at torus-boundaries. A higher-dimensional version of the tube algebra then defines an algebraic structure which extends the Drinfel’d double. After studying the fusion of the torus-excitations, we construct a general basis of excited states supported by arbitrary surfaces with one direction compactified. Applications of such basis to lattice gauge theory are finally discussed.