Model wavefunctions for interfaces between lattice Laughlin states

Abstract

We study the interfaces between lattice Laughlin states at different fillings. We propose a class of model wavefunctions for such systems constructed using conformal field theory. We find a nontrivial form of charge conservation at the interface, similar to the one encountered in the field theory works from the literature. Using Monte Carlo methods, we evaluate the correlation function and entanglement entropy at the border. Furthermore, we construct the wavefunction for quasihole excitations and evaluate their mutual statistics with respect to quasiholes originating at the same or the other side of the interface. We show that some of these excitations lose their anyonic statistics when crossing the interface, which can be interpreted as impermeability of the interface to these anyons. Contrary to most of the previous works on interfaces between topological orders, our approach is microscopic, allowing for a direct simulation of e.g. an anyon crossing the interface. Even though we determine the properties of the wavefunction numerically, the closed-form expressions allow us to study systems too large to be simulated by exact diagonalization.

arXiv commentA number of changes were made in response to referees' comments: large parts of the text were rewritten, new results were added, some of the old results were reinterpreted, the discussion of connection to earlier works was expanded

References in corpus (100)

• Topological entanglement entropy
• Detecting topological order in a ground state wave function
• Fractional quantum Hall states at zero magnetic field
• 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
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Condensate induced transitions between topologically ordered phases
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Parafermionic edge zero modes in Z_n-invariant spin chains
• Fractional topological insulators
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Genons, twist defects, and projective non-Abelian braiding statistics
• Fractional Quantum Hall Effect in Optical Lattices
• Topological Nematic States and Non-Abelian Lattice Dislocations
• 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
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
• Realizing Fractional Chern Insulators with Dipolar Spins
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Fractional topological liquids with time-reversal symmetry and their lattice realization
• Theory of defects in Abelian topological states
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Anyon condensation and its applications
• Fractional topological superconductors with fractionalized Majorana fermions
• 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
• Classification of Topological Defects in Abelian Topological States
• Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model
• A theory of topological edges and domain walls
• Exact Matrix Product States for Quantum Hall Wave Functions
• Kramers Pairs of Majorana Fermions and Parafermions in Fractional Topological Insulators
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Infinite matrix product states, Conformal Field Theory and the Haldane-Shastry model
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Fractional quantum Hall states in lattices: Local models and physical implementation
• Boundary Degeneracy of Topological Order
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Entanglement through conformal interfaces
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Characterization and stability of a fermionic ν=1/3 fractional Chern insulator
• Optical lattice quantum Hall effect
• Monte Carlo Evaluation of Non-Abelian Statistics
• Matrix Product States for Trial Quantum Hall States
• Spurious Long-range Entanglement and Replica Correlation Length
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Quantum Computing with Parafermions
• Non-Abelian Braiding of Lattice Bosons
• Generalized ADE Classification of Gapped Domain Walls
• Composite fermion wave functions as conformal field theory correlators
• Topological phases in gapped edges of fractionalized systems
• Interactions along an Entanglement Cut in 2+1D Abelian Topological Phases
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Ground-state degeneracy for abelian anyons in the presence of gapped boundaries
• 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
• Non-Abelian anyons: when Ising meets Fibonacci
• Mapping the braiding properties of the Moore-Read state
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Entanglement spectroscopy of chiral edge modes in the Quantum Hall effect
• Characterization of quasiholes in fractional Chern insulators
• Model States for a Class of Chiral Topological Order Interfaces
• Symmetry-Protected Topological Interfaces and Entanglement Sequences
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Parafermionic wires at the interface of chiral topological states
• Parafermion supporting platform based on spin transitions in the fractional quantum Hall effect regime
• The modular S-matrix as order parameter for topological phase transitions
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Matrix Product State description of the Halperin States
• Matrix product state representation of non-Abelian quasiholes
• Matrix Product State Description and Gaplessness of the Haldane-Rezayi State
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion
• Universal Periods in Quantum Hall Droplets
• Families of Gapped Interfaces Between Fractional Quantum Hall States
• Matrix product state representation of quasielectron wave functions
• Parafermions, induced edge states and domain walls in the fractional quantum Hall effect spin transitions
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Lattice Laughlin states on the torus from conformal field theory
• Truncation of lattice fractional quantum Hall Hamiltonians derived from conformal field theory
• Parafermions in Hierarchical Fractional Quantum Hall States
• Quasielectrons in lattice Moore-Read models

Cited by in corpus (6)

• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• 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
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Dynamics of Quantum Hall Interfaces