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.

5 pages, 3 figures

References in corpus (5)

• Non-Abelian Anyons and Topological Quantum Computation
• Twisted Quantum Double Model of Topological Phases in Two--Dimension
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Experimental Identification of Non-Abelian Topological Orders on a Quantum Simulator
• Accessing topological order in fractionalized liquids with gapped edges

Cited by in corpus (4)

• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• Twisted Quantum Double Model of Topological Orders with Boundaries