Boundary Hamiltonian Theory for Gapped Topological Orders
Yuting Hu1, Yidun Wan1,2, Yong-Shi Wu3,1,2,4**
1Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433 2Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093 3State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433 4Department of Physics and Astronomy, University of Utah, Salt Lake City, Utah, 84112, USA
Abstract：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 string-net 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. The creation and hopping operators of boundary quasi-particles are constructed. It is found 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.
2017, Vol. 34 
