Gapped edges and Bose condensation in anyonic systems

Alexei Kitaev

Caltech, Pasadena, USA

Certain types of Abelian and non-Abelian anyons can form multiparticle wave functions that are essentially constant, like the wave function of a Bose condensate. Such anyonic condensate may be characterized by a commutative Frobenius algebra in the underlying unitary braided category, together with some local order parameter. The Landau theory of phase transition can be adapted to this situation. Frobenius algebras also occur in the description of "hard" edges without gapless modes.

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