Starting from Halperin multilayer systems we develop a hierarchical scheme, dubbed symmetrized multicluster construction, 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 A. Bochniak, Z. Nussinov, A. Seidel, and G. Ortiz, 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 (or the off-diagonal long-range 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.

• Received 16 August 2023
• Accepted 21 November 2023

DOI:https://doi.org/10.1103/PhysRevB.108.245123

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Published by the American Physical Society