Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study

TL;DR

This study uses Tree Tensor Network methods to numerically analyze quasihole excitations in a bosonic fractional Chern insulator, confirming their fractional charge and anyonic statistics through density measurements.

Contribution

It provides the first numerical proof of anyonic statistics of quasiholes in a realistic Hamiltonian for fractional Chern insulators using density measurements.

Findings

Quasiholes exhibit quantized fractional charge.

Quasihole statistics are confirmed to be anyonic.

Density measurements can probe quasihole statistics experimentally.

Abstract

We numerically investigate the properties of the quasihole excitations above the bosonic fractional Chern insulator state at filling $\nu = 1/2$, in the specific case of the Harper-Hofstadter Hamiltonian with hard-core interactions. For this purpose we employ a Tree Tensor Network technique, which allows us to study systems with up to $N=18$ particles on a $16 \times 16$ lattice and experiencing an additional harmonic confinement. First, we observe the quantization of the quasihole charge at fractional values and its robustness against the shape and strength of the impurity potentials used to create and localize such excitations. Then, we numerically characterize quasihole anyonic statistics by applying a discretized version of the relation connecting the statistics of quasiholes in the lowest Landau level to the depletions they create in the density profile [Macaluso et al., arXiv:1903.03011]. Our results give a direct proof of the anyonic statistics for quasiholes of fractional Chern insulators, starting from a realistic Hamiltonian. Moreover, they provide strong indications that this property can be experimentally probed through local density measurements, making our scheme readily applicable in state-of-the-art experiments with ultracold atoms and superconducting qubits.