Pattern-of-zeros approach to Fractional quantum Hall states and a classification of symmetric polynomial of infinite variables

Understand

Some purely chiral fractional quantum Hall states are described by symmetric or anti-symmetric polynomials of infinite variables.

• In this article, we review a systematic construction and classification of those fractional quantum Hall states and the corresponding polynomials of infinite variables, using the pattern-of-zeros approach.
• We discuss how to use patterns of zeros to label different fractional quantum Hall states and the corresponding polynomials.
• We also discuss how to calculate various universal properties (ie the quantum topological invariants) from the pattern of zeros.