Model wavefunctions for an interface between lattice Laughlin and Moore-Read states

Abstract

We use conformal field theory to construct model wavefunctions for a gapless interface between lattice versions of a bosonic Laughlin state and a fermionic Moore-Read state, both at $\nu =1/2$. The properties of the resulting model state, such as particle density, correlation function and Rényi entanglement entropy are then studied using the Monte Carlo approach. Moreover, we construct the wavefunctions also for anyonic excitations (quasiparticles and quasiholes). We study their density profile, charge and statistics. We show that, similarly to the Laughlin-Laughlin case studied earlier, some anyons (the Laughlin Abelian ones) can cross the interface, while others (the non-Abelian ones) lose their anyonic character in such a process. Also, we argue that, under an assumption of local particle exchange, multiple interfaces give rise to a topological degeneracy, which can be interpreted as originating from Majorana zero modes.

arXiv commentPublished in PRB. Changes include typos and minor mistakes, not influencing the results

References in corpus (65)

• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Fractional quantum Hall states of atoms in optical Lattices
• Models for gapped boundaries and domain walls
• Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
• Exotic non-Abelian anyons from conventional fractional quantum Hall states
• Condensate induced transitions between topologically ordered phases
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Fractional Quantum Hall Effect in Optical Lattices
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Topological boundary conditions in abelian Chern-Simons theory
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Realizing Fractional Chern Insulators with Dipolar Spins
• A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation
• Zoology of Fractional Chern Insulators
• Edge excitations of paired fractional quantum Hall states
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Anyon condensation and its applications
• Exact Parent Hamiltonian for the Quantum Hall States in a Optical Lattice
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• High field fractional quantum Hall effect in optical lattices
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• A theory of topological edges and domain walls
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Phase transitions in topological lattice models via topological symmetry breaking
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Optical lattice quantum Hall effect
• Quantum Computing with Parafermions
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Lattice Laughlin States of Bosons and Fermions at Filling Fractions $1/q$
• Interface Contributions to Topological Entanglement in Abelian Chern-Simons Theory
• Striped quantum Hall state in a half-filled Landau level
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Non-Abelian anyons: when Ising meets Fibonacci
• Energetics of Pfaffian-AntiPfaffian Domains
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Model States for a Class of Chiral Topological Order Interfaces
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Edge Probes of Topological Order
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Parafermionic wires at the interface of chiral topological states
• The modular S-matrix as order parameter for topological phase transitions
• Nested Topological Order
• Entanglement Entropy of Generalized Moore-Read Fractional Quantum Hall State Interfaces
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Model wavefunctions for interfaces between lattice Laughlin states
• Quasielectrons in lattice Moore-Read models
• Continuum limit of lattice quasielectron wavefunctions
• Topological entanglement entropy relations for multi phase systems with interfaces

Cited by in corpus (4)

• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Attractive Haldane bilayers for trapping non-Abelian anyons
• Chiral conformal field theory for topological states and the anyon eigenbasis on the torus
• Dynamics of Quantum Hall Interfaces