Symmetry-Protected Topological Interfaces and Entanglement Sequences

Abstract

Gapped interfaces (and boundaries) of two-dimensional (2D) Abelian topological phases are shown to support a remarkably rich sequence of 1D symmetry-protected topological (SPT) states. We show that such interfaces can provide a physical interpretation for the corrections to the topological entanglement entropy of a 2D state with Abelian topological order found in Ref.~\onlinecite{cano-2015}. The topological entanglement entropy decomposes as $\gamma ={\gamma }_a+{\gamma }_s$, where ${\gamma }_a>0$ only depends on universal topological properties of the 2D state, while a correction ${\gamma }_s>0$ signals the emergence of the 1D SPT state that is produced by interactions along the entanglement cut and provides a direct measure of the stabilizing symmetry of the resulting SPT state. A correspondence is established between the possible values of ${\gamma }_s$ associated with a given interface - which is named Boundary Topological Entanglement Sequence - and classes of 1D SPT states. We show that symmetry-preserving domain walls along such 1D interfaces (or boundaries) generally host localized parafermion-like excitations that are stable to local symmetry-preserving perturbations.

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Topological boundary conditions in abelian Chern-Simons theory
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Fractional topological superconductors with fractionalized Majorana fermions
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Rokhsar-Kivelson Models of Bosonic Symmetry-Protected Topological States
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification

Cited by in corpus (23)

• Spurious topological entanglement entropy from subsystem symmetries
• Local probe of bulk and edge states in a fractional Chern insulator
• Subsystem symmetry enriched topological order in three dimensions
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Model States for a Class of Chiral Topological Order Interfaces
• Multipartitioning topological phases by vertex states and quantum entanglement
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Universal lower bound on topological entanglement entropy
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Toy model of boundary states with spurious topological entanglement entropy
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Families of Gapped Interfaces Between Fractional Quantum Hall States
• Disentangling (2+1)d Topological States of Matter with the Entanglement Negativity
• Model wavefunctions for interfaces between lattice Laughlin states
• Parafermions in Hierarchical Fractional Quantum Hall States
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Stability of topological purity under random local unitaries
• Many-body systems with spurious modular commutators
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Confinement and Flux Attachment
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Theory of Hofstadter Superconductors
• Topological entanglement entropy meets holographic entropy inequalities