2014/10/31 by Zhao Liu, R. N. Bhatt, Nicolas Regnault · 32 citations
Mathematics · Physics and Astronomy · #Abelian group #Composite fermion #Condensed matter physics #Electron #Fractional quantum Hall effect #Geometry #Lattice (music) #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum mechanics #Quantum spin Hall effect #Topological Materials and Phenomena #Torus #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.91.045126
published in Physical Review B 91(4) (American Physical Society) · 8 pages, 7 figures, published version
openalex publication_date 2015/01/20 · arxiv created 2015/01/21 · arxiv updated 2015/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We provide a detailed study of the Abelian quasiholes of \ensuremathν=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.