A Chern-Simons effective field theory for the Pfaffian quantum Hall state |
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| Institution: | 1. Department of''Physics, University of''Illinois at Urbana-Champaign, Urbana, IL, 61801, USA;2. Institute for Theoretical Physics, University of California, Santa Barbara, CA, 93106-4030, USA;3. Department of Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, OXI 3NP, UK;4. School of Natural Sciences, Institute for Advanced Study, Olden Lane, Princeton, N.J. 08540, USA;1. INFN Lecce, Via Arnesano, Lecce (IT);2. University College London, Gower Street, London (UK);1. Department of Physics, University of California, Berkeley, CA 94720, USA;2. Materials Sciences Division, Lawrence Berkeley National Laboratories, Berkeley, CA 94720, USA;3. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University, 2575 Sand Hill Road, Menlo Park, CA 94025, USA |
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| Abstract: | We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory. |
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