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

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.

21 pages, RevTeX4

References in corpus (1)

• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime

Cited by in corpus (4)

• Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros
• Pfaffian statistics through adiabatic transport in the 1D coherent state representation
• Domain walls, fusion rules and conformal field theory in the quantum Hall regime
• Spin chain description of rotating bosons at $\nu =1$