We present microscopic, multiple Landau level, (frustrationfree and positive semidefinite) parent Hamiltonians whose ground states, realizing different quantum Hall fluids, are partonlike and whose excitations display either Abelian or nonAbelian braiding statistics. We prove ground state energy monotonicity theorems for systems with different particle numbers in multiple Landau levels, demonstrate Sduality in the case of toroidal geometry, and establish complete sets of zero modes of special Hamiltonians stabilizing partonlike states, specifically at filling factor
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Candidate local parent Hamiltonian for the 3/7 fractional quantum Hall effect
While a parent Hamiltonian for Laughlin wave function has been long known in terms of the Haldane pseudopotentials, no parent Hamiltonians are known for the lowestLandaulevel projected wave functions of the composite fermion theory at with . If one takes the two lowest Landau levels to be degenerate, the TrugmanKivelson 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 TrugmanKivelson interaction produces a large number of zero energy states at Landau level filling of 3/7. We propose that adding an appropriately constructed threebody interaction yields the unprojected 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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 Award ID(s):
 2037990
 NSFPAR ID:
 10480472
 Publisher / Repository:
 Physical Review B
 Date Published:
 Journal Name:
 Physical Review B
 Volume:
 108
 Issue:
 8
 ISSN:
 24699950
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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