Boundary Hamiltonian theory for gapped topological phases on an open surface

Understand

In this paper we propose a Hamiltonian approach to gapped topological phases on an open surface with boundary.

• Our setting is an extension of the Levin-Wen model to a 2d graph on the open surface, whose boundary is part of the graph.
• We systematically construct a series of boundary Hamiltonians such that each of them, when combined with the usual Levin-Wen bulk Hamiltonian, gives rise to a gapped energy spectrum which is topologically protected; and the corresponding wave functions are robust under changes of the underlying graph that maintain the spatial topology of the system.
• We derive explicit ground-state wavefunctions of the system and show that the boundary types are classified by Morita-equivalent Frobenius algebras.