Simulation of Anyons Using Symmetric Tensor Network Algorithms

Robert N. C. Pfeifer

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arXiv · 1202.1522

Simulation of Anyons Using Symmetric Tensor Network Algorithms

Robert N. C. Pfeifer

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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.

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Robert N. C. Pfeifer. 2012-02-07. Simulation of Anyons Using Symmetric Tensor Network Algorithms. https://arxiv.org/abs/1202.1522

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