Jain hierarchy for the fractional quantum Hall effect

We propose the effective hierarchical partition function which is able to describe both the Jain states and the Jain-type hierarchical states. Using this partition function (effective Lagrangian) we calculate the charge of the quasiparticle excitations. We show that the Jain-type hierarchical states are equivalent to the system of anyons in the external magnetic field.     

Fractional quantum Hall effect,Jain’s rule,and topological textures

It is demonstrated that Jain’s rule for determining fractions in the quantum Hall effect can be obtained without recourse to the phenomenological concept of composite fermions. The possibility of existence is considered for topologically nontrivial many-electron wave functions, whose group classification gives an indication of special values of electron density in the ground states separated by a gap from excited energies.