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.

arXiv comment5 pages, 3 figures

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Cited by in corpus (21)

• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Entanglement Entropy, Quantum Fluctuations, and Thermal Entropy in Topological Phases
• A systematic construction of gapped non-liquid states
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions
• Symmetry Fractionalized (Irrationalized) Fusion Rules and Two Domain-Wall Verlinde Formulae
• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Correspondence between bulk entanglement and boundary excitation spectra in 2d gapped topological phases
• Entanglement Entropy of Topological Orders with Boundaries
• From effective Hamiltonian to anomaly inflow in topological orders with boundaries
• Anyon exclusions statistics on surfaces with gapped boundaries
• Boundary topological entanglement entropy in two and three dimensions
• Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• The boundary phase transitions of the 2+1D ${\mathbb{Z}}_N$ topological order via topological Wick rotation
• Note on searching for critical lattice models as entropy critical points from strange correlator
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries