A classification of symmetric polynomials of infinite variables -- a construction of Abelian and non-Abelian quantum Hall states

TL;DR

This paper introduces a classification scheme for symmetric polynomials of infinite variables based on their zero patterns, leading to new non-Abelian quantum Hall states linked to parafermion conformal field theories.

Contribution

It proposes a novel classification method for symmetric polynomials of infinite variables and constructs new non-Abelian quantum Hall states from this framework.

Findings

Classification scheme based on zero patterns

Construction of non-Abelian quantum Hall states

Connection to parafermion conformal field theories

Abstract

Classification of complex wave functions of infinite variables is an important problem since it is related to the classification of possible quantum states of matter. In this paper, we propose a way to classify symmetric polynomials of infinite variables using the pattern of zeros of the polynomials. Such a classification leads to a construction of a class of simple non-Abelian quantum Hall states which are closely related to parafermion conformal field theories.