Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

Abstract

This work concerns Ising quasiholes in Moore-Read type lattice wave functions derived from conformal field theory. We commence with constructing Moore-Read type lattice states and then add quasiholes to them. By use of Metropolis Monte Carlo simulations, we analyze the features of the quasiholes, such as their size, shape, charge, and braiding properties. The braiding properties, which turn out to be the same as in the continuum Moore-Read state, demonstrate the topological attributes of the Moore-Read lattice states in a direct way. We also derive parent Hamiltonians for which the states with quasiholes included are ground states. One advantage of these Hamiltonians lies therein that we can now braid the quasiholes just by changing the coupling strengths in the Hamiltonian since the Hamiltonian is a function of the positions of the quasiholes. The methodology exploited in this article can also be used to construct other kinds of lattice fractional quantum Hall models containing quasiholes, for example investigation of Fibonacci quasiholes in lattice Read-Rezayi states.

arXiv comment20 pages, 6 figures

References in corpus (41)

• Non-Abelian Anyons and Topological Quantum Computation
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Observation of half-integer thermal Hall conductance
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Lectures on the Quantum Hall Effect
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• Local Charge of the nu=5/2 Fractional Quantum Hall State
• Landau-level-mixing and the ground state of the 5/2 quantum Hall effect
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Non-adiabatic Effects in the Braiding of Non-Abelian Anyons in Topological Superconductors
• The Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of Landau Level Mixing and Non-Zero Width
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• The Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
• How quickly can anyons be braided? Or: How I learned to stop worrying about diabatic errors and love the anyon
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Abelian and Non-Abelian States in $\nu =2/3$ Bilayer Fractional Quantum Hall Systems
• Fractional Quantum Hall Bilayers at Half-Filling: Tunneling-driven Non-Abelian Phase
• Exact parent Hamiltonians of bosonic and fermionic Moore-Read states on lattices and local models
• Evidence of a fractional quantum Hall nematic phase in a microscopic model
• Berry phase and model wavefunction in the half-filled Landau Level
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Imaging anyons with scanning tunneling microscopy
• Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Characterization of quasiholes in fractional Chern insulators
• Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors
• Detecting Non-Abelian Anyons by Charging Spectroscopy
• Lattice effects on Laughlin wave functions and parent Hamiltonians
• Chiral correlators of the Ising conformal field theory
• Anisotropy Driven Transition from Moore-Read State to Quantum Hall Stripes
• One-dimensional itinerant interacting non-Abelian anyons
• Spin Correlations and Topological Entanglement Entropy in a Non-Abelian Spin-1 Spin Liquid
• Braids and phase gates through high-frequency virtual tunneling of Majorana Zero Modes
• Many-body Lattice Wavefunctions From Conformal Blocks

Cited by in corpus (10)

• Recent Developments in Fractional Chern Insulators
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Tracing non-Abelian anyons via impurity particles
• Model wavefunctions for interfaces between lattice Laughlin states
• Quasielectrons in lattice Moore-Read models
• 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
• Robust translational invariance in topological bands against lattice potentials and disorders
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Exact Parent Hamiltonians for All Landau Level States in a Half-flux Lattice