Parafermionic states in rotating Bose-Einstein condensates

TL;DR

This paper explores the existence and properties of parafermionic states in rapidly rotating Bose-Einstein condensates, analyzing their overlaps, degeneracies, and non-Abelian quasihole statistics at specific filling factors.

Contribution

It provides a numerical study of parafermionic states in rotating BECs, evaluating overlaps, degeneracies, and the validity of the parafermion model at various filling factors.

Findings

Overlap between ground state and Read-Rezayi state depends on system size and interactions.

Degeneracy of quasihole states matches theoretical predictions by E. Ardonne.

Non-Abelian statistics are supported by the quasihole state analysis.

Abstract

We investigate possible parafermionic states in rapidly rotating ultracold bosonic atomic gases at lowest Landau level filling factor nu=k/2. We study how the system size and interactions act upon the overlap between the true ground state and a candidate Read-Rezayi state. We also consider the quasihole states which are expected to display non-Abelian statistics. We numerically evaluate the degeneracy of these states and show agreement with a formula given by E. Ardonne. We compute the overlaps between low-lying exact eigenstates and quasihole candidate wavefunctions. We discuss the validity of the parafermion description as a function of the filling factor.