A theory of topological edges and domain walls

Abstract

We investigate domain walls between topologically ordered phases in two spatial dimensions and present a simple but general framework from which their degrees of freedom can be understood. The approach we present exploits the results on topological symmetry breaking that we have introduced and presented elsewhere. After summarizing the method, we work out predictions for the spectrum of edge excitations and for the transport through edges in some representative examples. These include domain walls between the Abelian and non-Abelian topological phases of Kitaev's honeycomb lattice model in a magnetic field, as well as recently proposed domain walls between spin polarized and unpolarized non-Abelian fractional quantum Hall states at different filling fractions.

4 pages, 1 figure, latex

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Condensate induced transitions between topologically ordered phases
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Interferometry of non-Abelian Anyons
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Non-abelian statistics from an abelian model
• Nematic phases and the breaking of double symmetries
• The Zero Temperature Phase Diagram of the Kitaev Model

Cited by in corpus (29)

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• Electric-magnetic duality in the quantum double models of topological orders with gapped boundaries
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• A (Dummy's) Guide to Working with Gapped Boundaries via (Fermion) Condensation
• Ishibashi States, Topological Orders with Boundaries and Topological Entanglement Entropy
• Composing topological domain walls and anyon mobility
• String Condensations in 3+1D and Lagrangian Algebras
• Zero energy and chiral edge modes in a p-wave magnetic spin model
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Josephson Coupled Moore-Read States
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Interfaces and the extended Hilbert space of Chern-Simons theory
• Russian doll spectrum in a non-Abelian string-net ladder
• 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
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Dynamics of Quantum Hall Interfaces
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• 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
• Competing automorphisms and disordered Floquet codes
• A chain of strongly correlated SU(2)_4 anyons: Hamiltonian and Hilbert space of states
• Simplicity condition and boundary-bulk duality
• Fourier-transformed gauge theory models of three-dimensional topological orders with gapped boundaries