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Anyon braiding on a fractal lattice with a local Hamiltonian

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  • Sourav Manna, Max-Planck-Institute for the Physics of Complex Systems, Weizmann Institute of Science
  • ,
  • Callum W. Duncan, Max-Planck-Institute for the Physics of Complex Systems, University of Strathclyde
  • ,
  • Carrie A. Weidner
  • ,
  • Jacob F. Sherson
  • Anne E.B. Nielsen

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.

Original languageEnglish
Article numberL021302
JournalPhysical Review A
Publication statusPublished - Feb 2022

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© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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