Microscopic definitions of anyon data

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.Note that this definition is manifestly independent of the phases of the three movement operators since each operator appears on both the left and right hand side of (1.1). Thus, this definition succeeds in isolating the exchange statistics, R(a, a), from extraneous geometric phases. In this paper, we arXiv:1910.11353v1 [cond-mat.str-el]

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