Characterization of quasiholes in fractional Chern insulators

Abstract

We provide a detailed study of the Abelian quasiholes of ν = 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.

Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models

“…This is because the singularity in the continuum wavefunction is approached. Figure 2 also shows that the radius of the quasihole is only a bit larger in the lattice than it is in the continuum, which is in line with the results in [20].…”

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

“…3, we estimate the quasihole radius as R ≈ 1.73 B when two (221) quasiholes are on top of each other. Note that this value is obviously smaller than the size of a single (221) quasihole, but almost the same as the ν FQH = 1/2 Laughlin quasihole radius 21 . Such a reduction of the quasihole size is a result of the interplay between two quasiholes when their pinning potentials are dragged towards each other and finally located on top of each other.…”

“…As discussed in Ref. 21, this phase should be equal to ±2πq qh /(−e) due to the existence of an effective magnetic field in the unit cell, where q qh is the quasihole charge. Therefore, we expect a Berry phase ±2π/3 for |C| = 2 FCI quasiholes at ν FCI = 1/3, where the sign depends on the direction of the path enclosing a unit cell area.…”

Charge and statistics of lattice quasiholes from density measurements: A tree tensor network study

“…in Refs. [46,49]], only recently it has been discovered that, for FQH states in the lowest Landau level (LLL), these depletions encode information also on the QH anyonic statistics [59]. By considering the interacting HH model as a concrete example, here we provide numerical evidence that the experimental protocol proposed in Ref.…”

“…Some works focused on the numerical characterization of these states by inspecting key quantities such as the many-body Chern number, the particle entanglement spectrum, the behavior of the correlation functions and the topological entanglement entropy [41][42][43], while others proposed ex-perimentally applicable schemes to identify these elusive strongly correlated phases of matter [44,45]. Finally, growing attention has been given to FCI bulk excitations [46][47][48][49], which (similarly to those characterizing the FQH effect) display fractional charge and anyonic statistics.…”