Twodimensional electron systems subjected to high transverse magnetic fields can exhibit Fractional Quantum Hall Effects (FQHE). In the GaAs/AlGaAs 2D electron system, a double degeneracy of Landau levels due to electronspin, is removed by a small Zeeman spin splitting,
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
 Award ID(s):
 2029401
 NSFPAR ID:
 10478330
 Publisher / Repository:
 SciPost
 Date Published:
 Journal Name:
 SciPost Physics
 Volume:
 15
 Issue:
 2
 ISSN:
 25424653
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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