Microscopic definitions of anyon data
Abstract
We present microscopic definitions of both the -symbol and -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 -symbol and -symbol in several exactly solvable lattice models and edge theories. We also show that our definitions of the -symbol and -symbol satisfy the pentagon and hexagon equations, thereby providing a microscopic derivation of these fundamental constraints.
Cite
@article{arxiv.1910.11353,
title = {Microscopic definitions of anyon data},
author = {Kyle Kawagoe and Michael Levin},
journal= {arXiv preprint arXiv:1910.11353},
year = {2020}
}
Comments
24 pages, 29 figures