Families of Gapped Interfaces Between Fractional Quantum Hall States

Abstract

Some interfaces between two different topologically ordered systems can be gapped. In earlier work it has been shown that such gapped interfaces can themselves be effective one dimensional topological systems that possess localized topological modes in open boundary geometries. Here we focus on how this occurs in the context of an interface between two, single-component Laughlin states of opposite chirality, and with filling fractions ${\nu }_1=1/p$ and ${\nu }_2=1/p{n}^2$. While one type of interface in such systems has been previously studied, we show that allowing for edge reconstruction effects opens up a wide variety of possible gapped interfaces depending on the number of divisors of $n.$ We apply a complementary description of the ${\nu }_2=1/p{n}^2$ system in terms of Laughlin states coupled to a discrete gauge ${\mathbb{Z}}_n$ field. This enables us to identify possible interfaces to the ${\nu }_1$ system based on complete or partial confinement of this gauge field. We determine the tunneling properties, ground state degeneracy, and the nature of the non-Abelian zero modes of each interface in order to physically distinguish them.

arXiv comment9 pages, 4 figures

References in corpus (38)

• Non-Abelian Anyons and Topological Quantum Computation
• Unpaired Majorana fermions in quantum wires
• Models for gapped boundaries and domain walls
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Protected edge modes without symmetry
• Topological boundary conditions in abelian Chern-Simons theory
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Classification and analysis of two dimensional abelian fractional topological insulators
• Gate-Tunable Resonant Tunneling in Double Bilayer Graphene Heterostructures
• Theory of defects in Abelian topological states
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Tunable Fractional Quantum Hall Phases in Bilayer Graphene
• Fractional topological superconductors with fractionalized Majorana fermions
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• Classification of Topological Defects in Abelian Topological States
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Free parafermions
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids
• Boundary Degeneracy of Topological Order
• Stability of zero modes in parafermion chains
• Phase diagram of the $Z_3$ Parafermionic Chain with Chiral Interactions
• Topological phases in gapped edges of fractionalized systems
• Ground-state degeneracy for abelian anyons in the presence of gapped boundaries
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Parafermionic phases with symmetry-breaking and topological order
• Topological and symmetry broken phases of Z_N parafermions in one dimension
• Weak symmetry breaking in two dimensional topological insulators
• Symmetry Enriched Phases via Pseudo Anyon Condensation
• Anyonic Symmetries and Topological Defects in Abelian Topological Phases: an application to the $ADE$ Classification
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Parafermionic wires at the interface of chiral topological states
• Chirality-Protected Majorana Zero Modes at the Gapless Edge of Abelian Quantum Hall States
• Fermion Parity Flips and Majorana Bound States at twist defects in Superconducting Fractional Topological Phases

Cited by in corpus (8)

• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Entanglement bootstrap approach for gapped domain walls
• Seeing topological entanglement through the information convex
• Towards Non-Invertible Anomalies from Generalized Ising Models
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Model wavefunctions for interfaces between lattice Laughlin states
• Dynamics of Quantum Hall Interfaces