Numerical Analysis of Quasiholes of the Moore-Read Wavefunction

Abstract

We demonstrate numerically that non-Abelian quasihole excitations of the $\nu =5/2$ fractional quantum Hall state have some of the key properties necessary to support quantum computation. We find that as the quasihole spacing is increased, the unitary transformation which describes winding two quasiholes around each other converges exponentially to its asymptotic limit and that the two orthogonal wavefunctions describing a system with four quasiholes become exponentially degenerate. We calculate the length scales for these two decays to be ${\xi }_U\approx 2.7{\ell }_0$ and ${\xi }_E\approx 2.3{\ell }_0$ respectively. Additionally we determine which fusion channel is lower in energy when two quasiholes are brought close together.

4 pages, 3 figures

References in corpus (24)

• Non-Abelian Anyons and Topological Quantum Computation
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Resonantly-paired fermionic superfluids
• Interacting anyons in topological quantum liquids: The golden chain
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• A Class of $P,T$-Invariant Topological Phases of Interacting Electrons
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Probing Non-Abelian Statistics with QuasiParticle Interferometry
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Monte Carlo Evaluation of Non-Abelian Statistics
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Spectrum of the non-abelian phase in Kitaev's honeycomb lattice model
• A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States
• Inequivalent classes of interference experiments with non-abelian anyons
• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect

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• Majorana Zero Modes and Topological Quantum Computation
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
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• A Short Introduction to Topological Quantum Computation
• Splitting of Majorana modes due to intervortex tunneling in a p + ip superconductor
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Universal quantum computation on a semiconductor quantum wire network
• More Realistic Hamiltonians for the Fractional Quantum Hall Regime in GaAs and Graphene
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Tunneling of anyonic Majorana excitations in topological superconductors
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Correlation Lengths and Topological Entanglement Entropies of Unitary and Non-Unitary Fractional Quantum Hall Wavefunctions
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• Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model
• Implementing arbitrary phase gates with Ising anyons
• Non-Abelian Braiding of Lattice Bosons
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• Landau Level Quantization on the Sphere
• Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Disorder-induced Majorana metal in interacting non-Abelian anyon systems
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Non-Abelian Fractional Chern Insulators from Long-Range Interactions
• Quantum Hall quasielectron operators in conformal field theory
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases
• Splitting the Topological Degeneracy of non-Abelian Anyons
• Perturbed vortex lattices and the stability of nucleated topological phases
• Splitting and oscillation of Majorana zero modes in the p-wave BCS-BEC evolution with plural vortices
• Exact Solution for Bulk-Edge Coupling in the Non-Abelian $\nu =5/2$ Quantum Hall Interferometer
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• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
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• Anyonic entanglement renormalization
• Fusion channels of non-Abelian anyons from angular-momentum and density-profile measurements
• Majorana fermions on a disordered triangular lattice
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Structure and consequences of vortex-core states in p-wave superfluids
• Enhanced bulk-edge Coulomb coupling in Fractional Fabry-Perot interferometers
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Detecting Non-Abelian Anyons by Charging Spectroscopy
• Skyrmions in the Moore-Read state at nu=5/2
• Tunable Splitting of the Ground-State Degeneracy in 1D Parafermionic Wires
• 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
• Tracing non-Abelian anyons via impurity particles
• Change in the character of quasiparticles without gap collapse in a model of fractional quantum Hall effect
• Rigorous Calculations of Non-Abelian Statistics in the Kitaev Honeycomb Model
• Strong-disorder renormalization for interacting non-Abelian anyon systems in two dimensions
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• 3- and 4-body Interactions from 2-body interactions in Spin Models: A Route to Abelian and Non-Abelian Fractional Chern Insulators
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
• Adiabatic Cooling with Non-Abelian Anyons
• Matrix product state representation of quasielectron wave functions
• Topological blockade and measurement of topological charge
• Compass and Kitaev models -- Theory and Physical Motivations
• Effect of thermal fluctuations in topological p-wave superconductors
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Model wavefunctions for interfaces between lattice Laughlin states
• Scaling and non-Abelian signature in fractional quantum Hall quasiparticle tunneling amplitude
• Edge-Induced Qubit Polarization in Systems with Ising Anyons
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Splitting of roton minimum in the ν=5/2 Moore-Read state
• Non-Abelian Majorana fermions in topological $s$-wave Fermi superfluids
• Braiding Flux-Tubes in Topological Quantum and Classical Lattice Models from Class-D
• Cotunneling in the ν= 5/2 fractional quantum Hall regime