Anyon braiding on a fractal lattice with a local Hamiltonian

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Manna, Sourav and Duncan, Callum W. and Weidner, Carrie A. and Sherson, Jacob F. and Nielsen, Anne E. B. (2022) Anyon braiding on a fractal lattice with a local Hamiltonian. Physical Review A, 105 (2). L021302. ISSN 2469-9926 (https://doi.org/10.1103/PhysRevA.105.L021302)

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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.

ORCID iDs

Manna, Sourav, Duncan, Callum W. ORCID logoORCID: https://orcid.org/0000-0003-3625-9842, Weidner, Carrie A., Sherson, Jacob F. and Nielsen, Anne E. B.;
  • Item type:Article
    ID code:79685
    Dates:
    Date
    Event
    18 February 2022
    Published
    31 January 2022
    Accepted
    Subjects:Science > Physics
    Department:Faculty of Science > Physics
    Depositing user: Pure Administrator
    Date deposited:22 Feb 2022 12:00
    Last modified:11 Nov 2024 13:24
    URI:https://strathprints.strath.ac.uk/id/eprint/79685
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