2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states

Abstract

By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wave functions for the v = 12 Pfaffian paired Hall state exhibit an exponential degeneracy at fixed positions. Indeed, we conjecture that for 2n quasiholes the states realize a spinor representation of an expanded (continuous) non-Abelian statistics group SO(2n). In the four-quasihole case, this is supported by an explicit calculation of the corresponding conformal blocks in the c = 12 + 1 conformal field theory. We present an argument for the universality of this result, which is significant for the foundations of fractional statistics generally. We note, for annular geometry, an amusing analog to black hole entropy. We predict, as a generic consequence, glassy behavior. Many of our considerations also apply to a form of the (3, 3, 1) state.