Physics – Condensed Matter
Scientific paper
1996-05-23
Physics
Condensed Matter
38 pages, no figures, phyzzx
Scientific paper
10.1016/0550-3213(96)00430-0
By explicitly identifying a basis valid for any number of electrons, we demonstrate that simple multi-quasihole wavefunctions for the $\nu=1/2$ 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.
Nayak Chetan
Wilczek Frank
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