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Quantum Physics, quant-ph
Abstract:
Starting from Halperin multilayer systems we develop a hierarchical scheme
that generates, bosonic and fermionic, single-layer quantum Hall states (or
vacua) of arbitrary filling factor. Our scheme allows for the insertion of
quasiparticle excitations with either Abelian or non-Abelian statistics and
quantum numbers that depend on the nature of the original vacuum. Most
importantly, it reveals a fusion mechanism for quasielectrons and
magnetoexcitons that generalizes ideas about particle fractionalization
introduced in Commun. Phys. 5, 171 (2022) for the case of Laughlin fluids. In
addition, in the second quantization representation, we uncover the inherent
topological quantum order characterizing these vacua. In particular, we
illustrate the methodology by constructing generalized composite (generalized
Read) operators for the non-Abelian Pfaffian and Hafnian quantum fluid states.
