Simulation of Anyons Using Symmetric Tensor Network Algorithms
arXiv:1202.1522
Abstract
In this thesis I develop a formalism whereby a tensor network may be understood in terms of a unitary braided tensor category, and represented in a particularly efficient manner corresponding to the exploitation of this mathematical structure. This approach permits the exploitation of the global Abelian and non-Abelian internal group symmetries of a lattice model, both to facilitate the study of particular symmetry sectors and to provide a considerable reduction in computational cost. It also enables the study of models with non-trivial exchange statistics (fermions, Abelian and non-Abelian anyons) using tensor network algorithms which scale polynomially in the system size.
PhD thesis, 220 pages, 7 tables, 76 figures, LaTeX2e; total size 2.7Mb as a PDF. Section 4.7 contains practical techniques for the implementation of anyonic tensor networks which have not been published elsewhere. v2: Fixed error in Fig. 2.5 which caused it to display incorrectly in Adobe Reader
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