FQHE and Jain's approach on the torus

TL;DR

This paper extends Jain's composite fermion approach to the fractional quantum Hall effect on a torus, using explicit wave functions and exploring connections with hierarchical schemes and conformal field theories.

Contribution

It introduces a redefinition of the vacuum state for composite fermions on a torus, enabling the application of Jain's idea in this geometry.

Findings

Realization of Jain's approach on a torus using explicit wave functions

Connection established between the composite fermion approach and hierarchical schemes

Discussion of the relation with $W_{1+ abla}$ algebras and conformal field theories

Abstract

By using the explicit knowledge of the lowest energy single particle wave functions in the presence of an {\it arbitrary} magnetic field, we extend to the case of a torus Jain's idea of looking at the FQHE as a manifestation of an integer effect for {\it composite fermions}. We show that this can be realized thanks to a redefinition of the vacuum state that is explicitly collective in nature. We also discuss the relationship of this approach with the hierarchical scheme and with the characterization of the Hall states in terms of $W_{1+\infty}$ algebras and 2D conformal field theories.