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

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.

13 pages (incl appendix), 7 figures -- updated references -- to be published in Phys. Rev. Research

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• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Anyonic molecules in atomic fractional quantum Hall liquids: a quantitative probe of fractional charge and anyonic statistics
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• Characterizing fractional topological phases of lattice bosons near the first Mott lobe
• Linear and nonlinear edge dynamics of trapped fractional quantum Hall droplets
• Growing Extended Laughlin States in a Quantum Gas Microscope: A Patchwork Construction
• Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
• Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe${}_2$
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Optimal control for preparing fractional quantum Hall states in optical lattices
• Numerical demonstration of Abelian fractional statistics of composite fermions in the spherical geometry
• Structure of the nearly-degenerate manifold of lattice quasiholes on a torus
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids
• Laughlin's quasielectron as a non-local composite fermion
• Measurable fractional spin for quantum Hall quasiparticles on the disk
• Bulk density signatures of a lattice quasihole with very few particles
• Simulating Quantum Circuits with Tree Tensor Networks using Density-Matrix Renormalization Group Algorithm
• Dynamics of quasiholes and quasiparticles at the edges of small lattices
• Spin fractionalization at the edge of quantum Hall fluids induced by bulk quasiparticles
• Hall-on-Toric: Descendant Laughlin state in the chiral ${\mathbb{Z}}_p$ toric code