Statistics of skyrmions and the 5/2 puzzle

TL;DR

This paper investigates the topology-dependent statistics of skyrmions, analyzes textured quasiholes, and constructs a wave function for the 5/2 quantum Hall state, revealing nuanced quantum statistical behaviors.

Contribution

It introduces a new perspective on skyrmion statistics, constructs textured two-hole eigenstates, and proposes a wave function for the 5/2 state based on these insights.

Findings

Statistics of quasiholes depends on skyrmion topology

Existence of textured two-hole Coulomb eigenstates without definite quantum statistics

A new wave function for the 5/2 state is constructed

Abstract

1) For the hard core interaction there is some freedom left in the choice of the exact multiskyrmionic wave function's topology. The statistics of textured quasiholes, analyzed by calculation of the Berry phase, depends on this choice of topology. 2) We find a class of textured two-hole eigenstates of the Coulomb interaction. There is no definite quantum statistics but there is a definite rule of how to construct Coulomb eigenstates out of the hard core wave functions. 3) A wave function for the 5/2 state is constructed according to this rule.