
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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License | CC BY 4.0 (Attribution) |
Work Type | Article |
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Publication Date | August 21, 2023 |
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Deposited | October 19, 2023 |
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