Path Integral Representation for Composite Fermions and Bosons

TL;DR

This paper introduces a novel path integral framework for describing composite fermions and bosons in 2D electron systems, emphasizing electron-hole symmetry and cluster formations for fractional quantum Hall states.

Contribution

It presents a new path integral representation that captures electron-hole symmetry and cluster dynamics in composite particle descriptions of quantum Hall states.

Findings

Electron-hole attraction models electron-electron interactions.

Cluster formations correspond to fractional quantum Hall states.

Simplified formulation of composite Boson approach.

Abstract

The density matrix of the 2D system of spinless electrons confined to the lowest Landau level is expressed using both basis of states parametrized by electron locations and basis of states parametrized by hole locations. In this representation, the electron-electron repulsion can be viewed as an electron-hole attraction. Electron-hole pairs stabilized by this attraction provide a new formulation for Composite Fermions which fully respects particle-hole symmetry. This representation also allows a particularly simple formulation of the composite Boson approach of generic n =p/q incompressible states: The n =p/q state corresponds to the formation of clusters made up on p electrons and q-p holes and fractionally charged excitations correspond to the breaking of such clusters.