Exclusion Statistics of Quasiparticles in Condensed States of Composite Fermion Excitations

TL;DR

This paper investigates the exclusion statistics of quasiparticles across various condensed states of composite fermion excitations, providing a theoretical framework aligned with recent experimental findings in quantum Hall systems.

Contribution

It introduces a hierarchy of condensed states of excitations in boson Jain states and derives the exclusion statistics of quasiparticles within this framework.

Findings

Exclusion statistics of quasiparticles is established at all hierarchy levels.

Quantum Hall states of charged $ extalpha$-anyons are described as incompressible states of $( extalpha+2p)$-anyons.

The framework aligns with recent experimental indications of composite fermion excitations.

Abstract

The exclusion statistics of quasiparticles is found at any level of the hierarchy of condensed states of composite fermion excitations (for which experimental indications have recently been found). The hierarchy of condensed states of excitations in boson Jain states is introduced and the statistics of quasiparticles is found. The quantum Hall states of charged $\alpha$-anyons ($\alpha$ -- the exclusion statistics parameter) can be described as incompressible states of $(\alpha+2p)$-anyons ($2p$ -- an even number).