| To study gapped topological phases on open surfaces with boundary, we propose to add appropriately
constructed boundary terms in the Hamiltonian. Our setting is exactly solvable discrete models, such as string-net models (andWitten
Dijkgraaf models). The full Hamiltonian in our approach yields a topologically protected, gapped
energy spectrum, with the corresponding wave functions robust under topologypreserving transformations of the
lattice.We explicitly present the wavefunctions of the ground states and boundary elementary excitations, as well as
creation and hopping operators of boundary quasiparticles. We find that given a bulk topological order, the gapped
boundary conditions are described by Frobenius algebras in its input data. Emergent topological properties of the
ground states and boundary excitations are described by (bi-) modules over Frobenius algebras. |
