Extend The Levin-Wen Model To Two-dimensional Topological Orders With Gapped Boundary Junctions

Abstract

A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of realizing topological quantum computation. To facilitate the study of such boundary defects, in this paper, we construct an exactly solvable Hamiltonian model of topological orders with gapped boundary junctions, where the boundary defects reside, by placing the Levin-Wen model on a disk, whose gapped boundary is separated into multiple segments by junctions. We find that the Hamiltonian of a gapped boundary junction is characterized by either a morphism between or a common Frobenius subalgebra of the two Frobenius algebras (in the input fusion category) characetrizing the two boundary segments joint by the junction. We derive a formula of the ground state degeneracy and an explicit ground-state basis of our model. We propose the notion of mobile and immobile charges on the boundary and find that they are quantum observables and label the ground-state basis. Our model is computation friendly.

arXiv commentVersion appearing in JHEP

References in corpus (30)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Models for gapped boundaries and domain walls
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• TFT construction of RCFT correlators I: Partition functions
• Duality and defects in rational conformal field theory
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• TFT construction of RCFT correlators III: Simple currents
• Theory of defects in Abelian topological states
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Lattice Topological Field Theory in Two Dimensions
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Generalized ADE Classification of Gapped Domain Walls
• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Ground-state degeneracy for abelian anyons in the presence of gapped boundaries
• Boundary Hamiltonian theory for gapped topological phases on an open surface
• On Defects Between Gapped Boundaries in Two-Dimensional Topological Phases of Matter
• Twisted Quantum Double Model of Topological Orders with Boundaries
• Symmetry Enriched Phases via Pseudo Anyon Condensation
• Revisiting Entanglement Entropy of Lattice Gauge Theories
• Boundary Hamiltonian theory for gapped topological orders
• Topological Quantum Computation with Gapped Boundaries
• A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation
• Anyon Condensation: Coherent states, Symmetry Enriched Topological Phases, Goldstone Theorem, and Dynamical Rearrangement of Symmetry
• Computing data for Levin-Wen with defects
• Nested Topological Order
• Fusing Binary Interface Defects in Topological Phases: The $\mathrm{Vec}(\mathbb{Z}/p\mathbb{Z})$ case
• Anyon exclusions statistics on surfaces with gapped boundaries

Cited by in corpus (5)

• Characteristic Properties of a Composite System of Topological Phases Separated by Gapped Domain Walls via an Exactly Solvable Hamiltonian Model
• Precision Higgs Boson Probe of Type-II Seesaw Models
• Nonabelian Anyon Condensation in 2+1d topological orders: A String-Net Model Realization
• Classification of Gapped Domain Walls of Topological Orders in 2+1 dimensions: A Levin-Wen Model Realization
• Noninvertible Gauge Symmetry in (2+1)d Topological Orders: A String-Net Model Realization