Hierarchy wave functions--from conformal correlators to Tao-Thouless states

TL;DR

This paper generalizes hierarchy wave functions for quantum Hall states using conformal field theory, showing their relation to Tao-Thouless states on a cylinder and connecting to composite fermion theory and fractional statistics.

Contribution

It introduces a new class of hierarchy wave functions based on successive quasielectron condensation, extending previous conformal field theory constructions.

Findings

Wave functions approach Tao-Thouless states on a thin cylinder.

Connection established with Wen's classification of quantum Hall fluids.

Discussion on fractional statistics and composite fermion descriptions.

Abstract

Laughlin's wave functions, describing the fractional quantum Hall effect at filling factors $\nu=1/(2k+1)$, can be obtained as correlation functions in conformal field theory, and recently this construction was extended to Jain's composite fermion wave functions at filling factors $\nu=n/(2kn+1)$. Here we generalize this latter construction and present ground state wave functions for all quantum Hall hierarchy states that are obtained by successive condensation of quasielectrons (as opposed to quasiholes) in the original hierarchy construction. By considering these wave functions on a cylinder, we show that they approach the exact ground states, the Tao-Thouless states, when the cylinder becomes thin. We also present wave functions for the multi-hole states, make the connection to Wen's general classification of abelian quantum Hall fluids, and discuss whether the fractional statistics of the quasiparticles can be analytically determined. Finally we discuss to what extent our wave functions can be described in the language of composite fermions.