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

Xiao-Gang Wen, Zhenghan Wang

Published 2008-03-07, updated 2008-05-03Version 3

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.