The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $\nu =2+⅗$, and thereby also its hole conjugate at $2+⅖$. We study a general class of tripartite composite fermion wave functions, which reduce to the Rezayi-Read 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 four-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+⅗$, and find reasonably good agreement. The ground state as well as several excited states of the four-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 $2+⅖$ and $2+⅗$ 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.

• Received 28 January 2013

DOI:https://doi.org/10.1103/PhysRevB.87.245125