1996/05/23 by Chetan Nayak, Frank Wilczek · 29 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conformal field theory #Conjecture #Degeneracy (biology) #Pfaffian #Quantum Hall effect #Quantum and electron transport phenomena #Spinor #Spinor field #State (computer science) #Topological Materials and Phenomena #Universality (dynamical systems) #cond-mat
paper · pdf · doi:10.1016/0550-3213(96)00430-0
38 pages, no figures, phyzzx
arxiv created 1996/05/23 · openalex publication_date 1996/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wavefunctions for the ν=1/2 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) nonabelian statistics group SO(2n). In the four quasihole case, this is supported by an explicit calculation of the corresponding conformal blocks in the c=1\over2+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 analogue 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.