Exactly solvable Hamiltonian for non-Abelian quasiparticles

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three-body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles. We further demonstrate, for systems for which exact diagonalization is possible, adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level Pfaffian Hamiltonian.

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Work Title Exactly solvable Hamiltonian for non-Abelian quasiparticles
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Open Access
Creators
  1. Koji Kudo
  2. A. Sharma
  3. G. J. Sreejith
  4. Jainendra Jain
License CC BY 4.0 (Attribution)
Work Type Article
Acknowledgments
  1. National Science Foundation under Grant No. DMR-2037990
Publisher
  1. Physical Review B
Publication Date March 29, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1103/PhysRevB.107.115163
Deposited October 19, 2023

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Version 1
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  • Updated Acknowledgments Show Changes
    Acknowledgments
    • National Science Foundation under Grant No. DMR-2037990
  • Added Creator Jainendra Jain
  • Added Exact-non-Abelian.pdf
  • Updated License Show Changes
    License
    • https://creativecommons.org/licenses/by/4.0/
  • Published
  • Updated Publisher, Publisher Identifier (DOI), Related URLs, and 1 more Show Changes
    Publisher
    • Physical Review B
    Publisher Identifier (DOI)
    • 10.1103/PhysRevB.107.115163
    • https://doi.org/10.1103/PhysRevB.107.115163
    Related URLs
    • https://journals.aps.org/prb/abstract/10.1103/PhysRevB.107.115163
    Publication Date
    • 2023
    • 2023-03-29
  • Updated Creator Jainendra Jain
  • Added Creator Koji Kudo
  • Added Creator A. Sharma
  • Added Creator G. J. Sreejith
  • Updated