Jain hierarchy for the Fractional Quantum Hall Effect

TL;DR

This paper introduces an effective hierarchical partition function to describe Jain states and Jain-type hierarchical states in the Fractional Quantum Hall Effect, providing a unified framework and calculating quasiparticle charges.

Contribution

It proposes a novel effective Lagrangian that captures both Jain and Jain-type hierarchical states, linking them to anyon systems in magnetic fields.

Findings

Effective partition function describes Jain states and hierarchical states.

Calculated quasiparticle charges within the framework.

Established equivalence between Jain-type states and anyon systems.

Abstract

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.