Microscopic definitions of anyon data

Kyle Kawagoe; Michael Levin

doi:10.1103/physrevb.101.115113

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arXiv · 1910.11353

Microscopic definitions of anyon data

Kyle Kawagoe·Michael Levin

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Abstract

We present microscopic definitions of both the $F$-symbol and $R$-symbol -- two pieces of algebraic data that characterize anyon excitations in (2+1)-dimensional systems. An important feature of our definitions is that they are operational; that is, they provide concrete procedures for computing these quantities from microscopic models. In fact, our definitions, together with known results, provide a way to extract a complete set of anyon data from a microscopic model, at least in principle. We illustrate our definitions by computing the $F$-symbol and $R$-symbol in several exactly solvable lattice models and edge theories. We also show that our definitions of the $F$-symbol and $R$-symbol satisfy the pentagon and hexagon equations, thereby providing a microscopic derivation of these fundamental constraints.

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Kyle Kawagoe, Michael Levin. 2019-10-24. Microscopic definitions of anyon data. https://doi.org/10.1103/physrevb.101.115113

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