A plasma analogy and Berry matrices for non-abelian quantum Hall states |
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| Institution: | 1. Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA;2. Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA;1. An Giang University, 18-Ung Van Khiem Street, Long Xuyen, An Giang, Viet Nam;2. Vietnam National University, Ho Chi Minh City, Viet Nam;1. Department of Physics, University of Ottawa, Ottawa, ON K1N 6N5, Canada;2. Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA;1. Institute of Automation and Control Processes FEB RAS, 5 Radio Street, 690041 Vladivostok, Russia;2. School of Natural Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia;3. Department of Electronics, Vladivostok State University of Economics and Service, 690600 Vladivostok, Russia |
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| Abstract: | We present an approach to the computation of the non-abelian statistics of quasiholes in quantum Hall states, such as the Pfaffian state, whose wavefunctions are related to the conformal blocks of minimal model conformal field theories. We use the Coulomb gas construction of these conformal field theories to formulate a plasma analogy for the quantum Hall states. A number of properties of the Pfaffian state follow immediately, including the Berry phases, which demonstrate the quasiholes' fractional charge, the abelian statistics of the two-quasihole state, and equal-time ground state correlation functions. The non-abelian statistics of multi-quasihole states follows from an additional assumption. |
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