HIDDEN MASSIVE DIRAC FERMIONS IN EFFECTIVE-FIELD THEORY FOR INTEGRAL QUANTUM HALL TRANSITIONS

Integral quantum Hall plateau transitions in a planar lattice system d ue to gap collapse can be described by an effective field theory with Dirac fermions. We discuss how to reproduce the correct integral value s for the Hall conductance sigma(xy) before and after the plateau tran sition, which are dictated by the microscopic topological invariant. I n addition to the massless Dirac fermions that appear at gap closing, the matching condition of sigma(xy) requires the introduction of massi ve Dirac fermions, as ''spectators,'' in the effective field theory. F or noninteracting electrons on the lattice, we give a general prescrip tion to determine these massive spectators, based on microscopic infor mation on the vortices in the magnetic Brillouin zone which are closel y related to edge states. Our description is demonstrated in a model w ith both nearest-neighbor and next-nearest-neighbor hoppings.