Explicit monodromy of Moore-Read wave functions on a torus

Abstract

We construct the wave functions for the Moore-Read $\nu =5/2$ quantum Hall state on a torus in the presence of two quasiholes. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. The result agrees with the recent discussion by Oshikawa {\it et al.} Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in some of the ground states.

34 pages, latex References updated, grammar and typos corrected

References in corpus (3)

• Towards Universal Topological Quantum Computation in the $\nu =5/2$ Fractional Quantum Hall State
• Fractionalization, topological order, and quasiparticle statistics
• Wavefunctions for topological quantum registers

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