1 research outputs found
Non-Abelian Quantum Hall States and their Quasiparticles: from the Pattern of Zeros to Vertex Algebra
In the pattern-of-zeros approach to quantum Hall states, a set of data
{n;m;S_a|a=1,...,n; n,m,S_a in N} (called the pattern of zeros) is introduced
to characterize a quantum Hall wave function. In this paper we find sufficient
conditions on the pattern of zeros so that the data correspond to a valid wave
function. Some times, a set of data {n;m;S_a} corresponds to a unique quantum
Hall state, while other times, a set of data corresponds to several different
quantum Hall states. So in the latter cases, the patterns of zeros alone does
not completely characterize the quantum Hall states. In this paper, We find
that the following expanded set of data {n;m;S_a;c|a=1,...,n; n,m,S_a in N; c
in R} provides a more complete characterization of quantum Hall states. Each
expanded set of data completely characterize a unique quantum Hall state, at
least for the examples discussed in this paper. The result is obtained by
combining the pattern of zeros and Z_n simple-current vertex algebra which
describes a large class of Abelian and non-Abelian quantum Hall states
\Phi_{Z_n}^sc. The more complete characterization in terms of {n;m;S_a;c}
allows us to obtain more topological properties of those states, which include
the central charge c of edge states, the scaling dimensions and the statistics
of quasiparticle excitations.Comment: 42 pages. RevTeX