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arXiv · 2305.12400

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

Koji Kudo·A. Sharma·G. J. Sreejith·J. K. Jain
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Abstract

While a parent Hamiltonian for 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 $n\geq2$. 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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Koji Kudo, A. Sharma, G. J. Sreejith, J. K. Jain. 2023-09-04. Candidate local parent Hamiltonian for 3/7 fractional quantum Hall effect. https://doi.org/10.1103/physrevb.108.085130

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