Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros

TL;DR

This paper extends the pattern of zeros classification to multilayer fractional quantum Hall states, leading to new non-Abelian states related to affine Lie algebra conformal field theories, with potential experimental relevance.

Contribution

It generalizes the pattern of zeros approach to multilayer FQH states and constructs a new class of non-Abelian states linked to affine Lie algebra conformal field theories.

Findings

Classified multilayer FQH states using pattern of zeros.

Constructed non-Abelian multilayer FQH states related to affine Lie algebras.

Discussed experimental possibilities in bilayer FQH systems.

Abstract

A large class of fractional quantum Hall (FQH) states can be classified according to their pattern of zeros, which describes the way ideal ground state wave functions go to zero as various clusters of electrons are brought together. In this paper we generalize this approach to classify multilayer FQH states. Such a classification leads to the construction of a class of non-Abelian multilayer FQH states that are closely related to $\hat{g}_k$ parafermion conformal field theories, where $\hat{g}_k$ is an affine simple Lie algebra. We discuss the possibility of some of the simplest of these non-Abelian states occuring in experiments on bilayer FQH systems at $\nu = 2/3$, 4/5, 4/7, etc.