Tripartite Composite Fermion States

TL;DR

This paper introduces a class of tripartite composite fermion wave functions that generalize the Read-Rezayi states, providing numerical evidence that they effectively describe the low-energy physics of fractional quantum Hall states at specific filling fractions.

Contribution

The authors develop and analyze tripartite composite fermion wave functions that interpolate between known states and excitations, offering a new approach to understanding fractional quantum Hall states at $ u=2+rac{3}{5}$ and $rac{2}{5}$.

Findings

Wave functions match well with low-energy states of a 4-body interaction.

Good agreement between tripartite wave functions and Coulomb eigenstates at $ u=2+rac{3}{5}$.

States evolve adiabatically from model to Coulomb interactions for N=15 particles.

Abstract

The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $\nu=2+\nicefrac{3}{5}$, and thereby also its hole conjugate at $2+\nicefrac{2}{5}$. We study a general class of "tripartite" composite fermion wave functions, which reduce to the Read-Rezayi ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a 4-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+\nicefrac{3}{5}$, and find reasonably good agreement. The ground state as well as several excited states of the 4-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for N=15 particles. These results support the plausibility of the Read-Rezayi proposal for the $2+\nicefrac{2}{5}$ and $2+\nicefrac{3}{5}$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.