Classification of Abelian and non-Abelian multilayer fractional quantum Hall states through the pattern of zeros

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 ̂ \^gₖ parafermion conformal field theories, where ̂ \^gₖ is an affine simple Lie algebra. We discuss the possibility of some of the simplest of these non-Abelian states occurring in experiments on bilayer FQH systems at ν=2/3, 4/5, 4/7, etc.