A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States

Details A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States A Plasma Analogy and Berry Matrices for Non-Abelian Quantum Hall States

1997-06-23

arxiv.org/abs/cond-mat/9706227v1

Nucl. Phys. B506, 685 (1997)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

7 pages, LaTeX

Scientific paper

10.1016/S0550-3213(97)00612-3

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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