Candidate local parent Hamiltonian for the 3/7 fractional quantum Hall effect

Although a parent Hamiltonian for the Laughlin 1/3 wave function has been long known in terms of the Haldane pseudopotentials, no parent Hamiltonians are known for the lowest-Landau-level projected wave functions of the composite fermion theory at n/(2n+1) with n≥2. If one takes the two lowest Landau levels to be degenerate, the Trugman-Kivelson interaction produces the unprojected 2/5 wave function as the unique zero energy solution. If the lowest three Landau levels are assumed to be degenerate, the Trugman-Kivelson interaction produces a large number of zero energy states at ν=3/7. We propose that adding an appropriately constructed three-body interaction yields the unprojected 3/7 wave function as the unique zero energy solution and report extensive exact diagonalization studies that provide strong support to this proposal.

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Work Title Candidate local parent Hamiltonian for the 3/7 fractional quantum Hall effect
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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 August 21, 2023
Publisher Identifier (DOI)
  1. https://doi.org/10.1103/PhysRevB.108.085130
Deposited October 19, 2023

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Version 1
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  • Created
  • Updated
  • Updated Acknowledgments Show Changes
    Acknowledgments
    • National Science Foundation under Grant No. DMR-2037990
  • Added Creator Jainendra Jain
  • Added exact-model-37.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.108.085130
    • https://doi.org/10.1103/PhysRevB.108.085130
    Related URLs
    • https://journals.aps.org/prb/abstract/10.1103/PhysRevB.108.085130
    Publication Date
    • 2023
    • 2023-08-21
  • Updated Creator Jainendra Jain
  • Added Creator Koji Kudo
  • Added Creator A. Sharma
  • Added Creator G. J. Sreejith
  • Updated