Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level

TL;DR

This paper develops a hierarchical scheme for generating quantum Hall states with quasiparticles of various statistics, revealing a fusion mechanism and topological order in the lowest Landau level, applicable to both Abelian and non-Abelian states.

Contribution

It introduces a new hierarchical scheme for creating quantum Hall states with quasiparticles, generalizing particle fractionalization and uncovering topological quantum order.

Findings

Fusion mechanism for quasielectrons and magnetoexcitons

Construction of generalized composite operators for non-Abelian states

Revelation of inherent topological quantum order

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 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 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.