Topological properties of Abelian and non-Abelian quantum Hall states from the pattern of zeros

TL;DR

This paper demonstrates how to derive topological properties of Abelian and non-Abelian quantum Hall states from their patterns of zeros, providing a systematic way to analyze their quasiparticle types and quantum numbers.

Contribution

It introduces a method to compute topological invariants of quantum Hall states directly from their pattern of zeros sequences {S_a}.

Findings

Calculated quasiparticle types and quantum numbers from {S_a}

Analyzed quasiparticle tunneling and modular transformations

Provided a framework for topological characterization of quantum Hall states

Abstract

It has been shown that different Abelian and non-Abelian fraction quantum Hall states can be characterized by patterns of zeros described by sequences of integers {S_a}. In this paper, we will show how to use the data {S_a} to calculate various topological properties of the corresponding fraction quantum Hall state, such as the number of possible quasiparticle types and their quantum numbers, as well as the actions of the quasiparticle tunneling and modular transformations on the degenerate ground states on torus.