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arXiv · 1310.6001

Diagrammatics for Bose condensation in anyon theories

I. S. Eliëns·J. C. Romers·F. A. Bais
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Abstract

Phase transitions in anyon models in (2+1)-dimensions can be driven by condensation of bosonic particle sectors. We study such condensates in a diagrammatic language and explicitly establish the relation between the states in the fusion spaces of the theory with the condensate, to the states in the parent theory using a new set of mathematical quantities called vertex lifting coefficients (VLCs). These allow one to calculate the full set of topological data ($S$-, $T$-, $R$- and $F$-matrices) in the condensed phase. We provide closed form expressions of the topological data in terms of the VLCs and provide a method by which one can calculate the VLCs for a wide class of bosonic condensates. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase, such that they can be evaluated using the data of the original theory and a limited number of VLCs. Some representative examples are worked out in detail.

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I. S. Eliëns, J. C. Romers, F. A. Bais. 2013-10-22. Diagrammatics for Bose condensation in anyon theories. https://doi.org/10.1103/physrevb.90.195130

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