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  • Letter
  • Open Access

Anyon braiding on a fractal lattice with a local Hamiltonian

Sourav Manna1,2, Callum W. Duncan1,3, Carrie A. Weidner4, Jacob F. Sherson4, and Anne E. B. Nielsen1,4

  • 1Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany
  • 2Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 7610001, Israel
  • 3Department of Physics, SUPA and University of Strathclyde, Glasgow G4 0NG, United Kingdom
  • 4Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C, Denmark

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Phys. Rev. A 105, L021302 – Published 18 February, 2022Erratum Phys. Rev. A 107, 069901 (2023)

DOI: https://doi.org/10.1103/PhysRevA.105.L021302

Abstract

There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. Here we construct a local Hamiltonian on a fractal lattice whose ground state exhibits topological braiding properties. The fractal lattice is obtained from a second-generation Sierpinski carpet with Hausdorff dimension 1.89. We use local potentials to trap and exchange anyons in the model, and the numerically obtained results for the exchange statistics of the anyons are close to the ideal statistics for quasiholes in a bosonic Laughlin state at half filling. For the considered system size, the energy gap is about three times larger for the fractal lattice than for a two-dimensional square lattice, and we find that the braiding results obtained on the fractal lattice are more robust against disorder. We propose a scheme to implement both fractal lattices and our proposed local Hamiltonian with ultracold atoms in optical lattices.

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Erratum

Erratum: Anyon braiding on a fractal lattice with a local Hamiltonian [Phys. Rev. A 105, L021302 (2022)]

Sourav Manna, Callum W. Duncan, Carrie A. Weidner, Jacob F. Sherson, and Anne E. B. Nielsen
Phys. Rev. A 107, 069901 (2023)

Article Text

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Phys. Rev. A 105, L021302– Published 18 February, 2022
  • Received 24 August 2021
  • Accepted 31 January 2022
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