Title: Boundary Hamiltonian theory for gapped topological orders,
Abstract: In this letter, we report our systematic construction of the lattice
Hamiltonian model of topological orders on open surfaces, with explicit
boundary terms. We do this mainly for the Levin-Wen stringnet model. The full
Hamiltonian in our approach yields a topologically protected, gapped energy
spectrum, with the corresponding wave functions robust under
topology-preserving transformations of the lattice of the system. We explicitly
present the wavefunctions of the ground states and boundary elementary
excitations. We construct the creation and hopping operators of boundary
quasi-particles. We find that given a bulk topological order, the gapped
boundary conditions are classified by Frobenius algebras in its input data.
Emergent topological properties of the ground states and boundary excitations
are characterized by (bi-) modules over Frobenius algebras.