Characterization of quasiholes in fractional Chern insulators

Abstract

We provide a detailed study of the Abelian quasiholes of $\nu =1/2$ bosonic fractional quantum Hall states on the torus geometry and in fractional Chern insulators. We find that the density distribution of a quasihole in a fractional Chern insulator can be related to that of the corresponding fractional quantum Hall state by choosing an appropriate length unit on the lattice. This length unit only depends on the lattice model that hosts the fractional Chern insulator. Therefore, the quasihole size in a fractional Chern insulator can be predicted for any lattice model once the quasihole size of the corresponding fractional quantum Hall state is known. We discuss the effect of the lattice embedding on the quasihole size. We also perform the braiding of quasiholes for fractional Chern insulator models to probe the fractional statistics of these excitations. The numerical values of the braiding phases accurately match the theoretical predictions.

8 pages, 7 figures, published version

References in corpus (24)

• Non-Abelian Anyons and Topological Quantum Computation
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Fractional Quantum Hall Effect in Optical Lattices
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Fractional Chern Insulators in Topological Flat bands with Higher Chern Number
• Topological flat band models with arbitrary Chern numbers
• Optical Flux Lattices for Ultracold Atomic Gases
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Flat bands with higher Chern number in pyrochlore slabs
• The non-Abelian Interferometer
• 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
• Degeneracy of non-abelian quantum Hall states on the torus: domain walls and conformal field theory
• Braiding non-Abelian quasiholes in fractional quantum Hall states
• The single-mode approximation for fractional Chern insulators and the fractional quantum Hall effect on the torus
• Anyon braiding in semi-analytical fractional quantum Hall lattice models
• Interacting bosons in topological optical flux lattices
• Localized quasiholes and the Majorana fermion in fractional quantum Hall state at nu=5/2 via direct diagonalization

Cited by in corpus (11)

• Recent Developments in Fractional Chern Insulators
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• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Squeezing anyons for braiding on small lattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Continuum limit of lattice quasielectron wavefunctions
• Stability of quasi-particle creation and multiband geometry in fractional Chern insulators under magnetic fields
• Bulk density signatures of a lattice quasihole with very few particles
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Spinless and spinful charge excitations in moiré Fractional Chern Insulators
• Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints