Modular transformation and bosonic/fermionic topological orders in Abelian fractional quantum Hall states

摘要: The non-Abelian geometric phases of the robust degenerate ground states were proposed as physically measurable defining properties topological order in 1990. In this paper we discuss detail such a quantitative characterization order, using generic Abelian fractional quantum Hall examples. We find way to determine even pure U(1) phase phases. show that not only contain information about quasi-particle statistics, they also chiral central charge Delta c mod 24 edge states, well viscosity. Thus, (both part and part) provide quite complete characterize 2D order.