Quasiparticle Interactions in Fractional Quantum Hall Systems: Justification of Different Hierarchy Schemes

TL;DR

This paper analyzes quasiparticle interactions in fractional quantum Hall systems, establishing rules for identifying incompressible states and confirming the Jain sequence as the primary hierarchy in the thermodynamic limit.

Contribution

It provides a theoretical justification for the Jain sequence hierarchy and clarifies the conditions under which different FQH states occur based on pseudopotential analysis.

Findings

Jain sequence states are the only incompressible states in the thermodynamic limit.

Other FQH hierarchy states can occur in finite systems.

The results support the composite Fermion model's validity.

Abstract

The pseudopotentials describing the interactions of quasiparticles in fractional quantum Hall (FQH) states are studied. Rules for the identification of incompressible quantum fluid ground states are found, based upon the form of the pseudopotentials. States belonging to the Jain sequence nu=n/(1+2pn), where n and p are integers, appear to be the only incompressible states in the thermodynamic limit, although other FQH hierarchy states occur for finite size systems. This explains the success of the composite Fermion picture.