Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands

Abstract

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu =1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ model state, we observe isotropic quasiholes with a clear internal structure, and obtain the quasihole charge and statistics matching the theoretical values. Interestingly, we also extract the same quasihole size, charge, and braiding statistics for the continuum model states of $|C|=2$ fractional Chern insulators, although the latter possess a "color-entangled" nature that does not exist in ordinary two-component Halperin states. We also consider two real lattice models with a band having $|C|=2$. There, we find that a quasihole can exhibit much stronger oscillations of the density profile, while having the same charge and statistics as those in the continuum models.

arXiv comment11 pages, 10 figures, small changes in the text related to the review process (mostly improved presentation of the color-entangled BC), added bibliographical details

References in corpus (60)

• Fault-tolerant quantum computation by anyons
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Topological orders and Edge excitations in FQH states
• Nearly-flat bands with nontrivial topology
• Zoo of quantum-topological phases of matter
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Fractional quantum Hall effect in the absence of Landau levels
• Fractional Chern Insulator
• Topological Flat Band Models and Fractional Chern Insulators
• Fractional Quantum Hall Physics in Topological Flat Bands
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Observation of fractional Chern insulators in a van der Waals heterostructure
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• Topological Nematic States and Non-Abelian Lattice Dislocations
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Zoology of Fractional Chern Insulators
• Topological flat band models with arbitrary Chern numbers
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Exact Matrix Product States for Quantum Hall Wave Functions
• Series of Abelian and Non-Abelian States in C>1 Fractional Chern Insulators
• The non-Abelian Interferometer
• Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
• Primary-Filling e/3 Quasiparticle Interferometer
• Fractional quantum Hall effect at $\nu =5/2$: Ground states, non-Abelian quasiholes, and edge modes in a microscopic model
• Hierarchy of fractional Chern insulators and competing compressible states
• Numerical Analysis of Quasiholes of the Moore-Read Wavefunction
• Gauge-Fixed Wannier Wave-Functions for Fractional Topological Insulators
• Adiabatic continuation of Fractional Chern Insulators to Fractional Quantum Hall States
• Monte Carlo Evaluation of Non-Abelian Statistics
• Fractional (Chern and topological) insulators
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• Non-Abelian Braiding of Lattice Bosons
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• Creating, probing, and manipulating fractionally charged excitations of fractional Chern insulators in optical lattices
• From fractional Chern insulators to Abelian and non-Abelian fractional quantum Hall states: adiabatic continuity and orbital entanglement spectrum
• ${\mathbb{Z}}_2$ fractional topological insulators in two dimensions
• Model Fractional Chern Insulators
• Haldane Statistics for Fractional Chern Insulators with an Arbitrary Chern number
• Minimal Entangled States and Modular Matrix for Fractional Quantum Hall Effect in Topological Flat Bands
• Telegraph noise and the Fabry-Perot quantum Hall interferometer
• Fermionizing a small gas of ultracold bosons
• 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
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Tunable Band Topology Reflected by Fractional Quantum Hall States in Two-Dimensional Lattices
• Characterization of quasiholes in fractional Chern insulators
• Fractional Topological Phases in Generalized Hofstadter Bands with Arbitrary Chern Numbers
• Fractional Chern Insulator phase at the transition between checkerboard and Lieb lattice
• Identifying Non-Abelian Topological Order through Minimal Entangled States
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization
• Imaging of quantum Hall states in ultracold atomic gases
• Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
• Investigation of trial wavefunction approach to bilayer Quantum Hall systems
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes

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• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Model wavefunctions for interfaces between lattice Laughlin states
• Bosonic fractional Chern insulating state at integer fillings in multi-band system
• Quasielectrons in lattice Moore-Read models
• Squeezing anyons for braiding on small lattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Interaction-driven transition between the Wigner crystal and the fractional Chern insulator in topological flat bands
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Measurable fractional spin for quantum Hall quasiparticles on the disk