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

Year: 2020

Authors: Macaluso E., Comparin T., Umucalilar RO., Gerster M., Montangero S., Rizzi M., Carusotto I.

Autors Affiliation: Univ Trento, INO CNR BEC Ctr, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Univ Lyon, Univ Claude Bernard, ENS Lyon, CNRS,Lab Phys, F-69342 Lyon, France; Mimar Sinan Fine Arts Univ, Dept Phys, TR-34380 Istanbul, Turkey; Univ Ulm, Inst Complex Quantum Syst, D-89069 Ulm, Germany; Univ Ulm, Ctr Integrated Quantum Sci & Technol, D-89069 Ulm, Germany; Univ Padua, Dipartimento Fis & Astron G Galilei, I-35131 Padua, Italy; Ist Nazl Fis Nucl, I-35131 Padua, Italy; Forschungszentrum Julich, Inst Quantum Control PGI 8, D-52425 Julich, Germany; Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany.

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 x 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 [E. Macaluso et al., Phys. Rev. Lett. 123, 266801 (2019)]. 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.

Journal/Review: PHYSICAL REVIEW RESEARCH

Volume: 2 (1)      Pages from: 13145-1  to: 13145-14

More Information: Discussions with L. Mazza, N. Regnault, and P. Roushan, and technical support from L. Parisi, are warmly acknowledged. E.M. also thanks M. Ra.ci unas and F. N. Unal for fruitful discussions and for sharing some of the data presented in Ref. [48]. E.M., T.C., and I.C. acknowledge financial support from the Provincia Autonoma di Trento and from Google via the quantum NISQ award. I.C. also acknowledges financial support from the FET-Open Grant MIR-BOSE (No. 737017) and Quantum Flagship Grant PhoQuS (No. 820392) of the European Union. R.O.U. has been supported by the BAGEP Award of the Science Academy (Turkey). S.M. acknowledges support from the DFG via TWITTER, the Italian PRIN 2017, and the EU via the PASQUANS and the QuantERA-QTFLAG projects. M.R. acknowledges support from the DFG via Grant No. RI 2345/2-1,from the EU via the PASQUANS project and from the Alexander von Humboldt foundation via the FeodorLynen Research Fellowship, and the hospitality of the INOCNR BEC Center at Trento. Part of the numerical calculations in this work has been performed with the computational resources provided by theMogon cluster at Johannes Gutenberg University, Mainz (hpc.uni-mainz.de) made available by the CSM and AHRP.
KeyWords: Quantum Hall States; Wave-functions; Electrons; Anyons; Parity; Model
DOI: 10.1103/PhysRevResearch.2.013145

Citations: 18
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