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.

arXiv comment8 pages, 7 figures, published version

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• 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
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Bosonic integer quantum Hall states in topological bands with Chern number two
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Real-space probe for lattice quasiholes
• Continuum limit of lattice models with Laughlin-like ground states containing quasiholes
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Model wavefunctions for interfaces between lattice Laughlin states
• Squeezing anyons for braiding on small lattices
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Anyonic quasiparticles of hardcore anyons
• 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