Field Theory of the Fractional Quantum Hall Effect-I

TL;DR

This paper develops a Chern-Simons field theory for fractional quantum Hall states, deriving wavefunctions, quasiparticle operators, and effective parameters, providing a detailed theoretical framework for understanding these complex quantum states.

Contribution

It introduces a comprehensive Chern-Simons theory incorporating magnetoplasmon modes and derives correlated wavefunctions and operators, advancing the theoretical understanding of fractional quantum Hall effects.

Findings

Derived correlated wavefunctions for fractional quantum Hall states

Constructed operators for quasiholes and composite particles

Calculated effective mass and charge renormalization

Abstract

We provide details of a shorter letter and cond-mat/9702098 and some new results. We describe a Chern-Simons theory for the fractional quantum Hall states in which magnetoplasmon degrees of freedom enter. We derive correlated wavefunctions, operators for creating quasiholes and composite fermions and bosons (which are electrons bound to zeros). We show how the charge of these particles and mass gets renormalized to the final values and compute the effective mass approximately. By deriving a hamiltonian description of the composite fermions and bosons and their charge and current operators, we make precise and reconcile many notions that have been associated with them.