Boundary Hamiltonian Theory for Gapped Topological Orders

作     者：胡愈挺 万义顿 吴咏时 

作者机构：Department of Physics and Center for Field Theory and Particle Physics Fudan University Collaborative Innovation Center of Advanced Microstructures State Key Laboratory of Surface PhysicsFudan University Department of Physics and AstronomyUniversity of Utah 

出 版 物：《Chinese Physics Letters》 (中国物理快报（英文版）)

年 卷 期：2017年第34卷第7期

页      面：207-211页

核心收录：

学科分类：07[理学] 070205[理学-凝聚态物理] 0702[理学-物理学] 

主　　题：Boundary Hamiltonian Theory for Gapped Topological Orders 

摘      要：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.