Connection between spin-singlet and hierarchical wave functions in the fractional quantum Hall effect

Abstract

We propose trial expressions for the many-body wave functions of the incompressible fluid states responsible for the fractional quantum Hall effect at filling factor $\nu$ not equal to $\frac{1}{m}$. For $\nu =\frac{q}{p}$, the wave functions are related to the wave functions for the total $S=0\mathrm{}$ states of objects with spin $\frac{\mathrm{}(q-1\mathrm{})\mathrm{}}{2}$. In particular, for $\nu =\frac{2}{5}$ the wave function is related to the total $S=0\mathrm{}$, $\nu =\frac{1}{2}$ hollow-core-model ground state recently discovered by Haldane and Rezayi.