Topological order and edge structure of ν = 1/2 quantum Hall state*

ABSTRACT: We study topological order and edge excitations of ν = 1/2 fractional quantum Hall state (FQH) of spin polarized electrons in single-layer system. We find that the 1/2 FQH state obtained in the numerical study of Greiter et al. has a non-abelian topological order suggested by Moore and Read. The edge excitations in such a non-abelian FQH state are found to be described by the U(1) Kac-Moody algebra plus an chiral Majorana fermion theory. The electron and the quasiparticle propagators are calculated. Some experimental consequences are also discussed. * Published in Phys. Rev. Lett. 70, 355 (1993) Spin polarized ν = 1/2 FQH states were recently observed in experiments in double-layer systems.1,2 The samples in Ref. 2 have a large interlayer hopping rate. The splitting between the symmetric and the anti-symmetric states is of order ∆SAS ∼ 10K. Thus the ν = 1/2 FQH state observed in Ref. 2 might correspond to a single-layer FQH state. The numerical calculations in Ref. 3 show that the 1/2 state is possible and likely to appear in single-layer system if the short range repulsion in the Coulomb interaction is reduced. An incompressible ν = 1/2 FQH state was found with an energy gap ∆ ∼ 0.1 in the thermodynamic limit, if the pseudo potential4 of the electron interaction is given by V1 = cos(φ), V3 = sin(φ), φ = 0.15pi. In this paper we are going to study the topological orders5 in this 1/2 FQH state. We will demonstrate how to use characteristics of finite-size systems to determine the topological orders in the 1/2 state. Our approach should also apply to other FQH states. Now it is well known that, at a given filling fraction, FQH states may have many different internal structures.6,5,7,8 The 1/2 FQH state in the V1-V3 model is likely to belong to one of the following universality classes: A) The ν = 1/8 Laughlin state of the charge 2e electron pairs.9,3 The effective theory of this state has a for