1202.1522 (Robert N. C. Pfeifer)

Simulation of Anyons Using Symmetric Tensor Network Algorithms    [PDF]

Robert N. C. Pfeifer

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.

View original: http://arxiv.org/abs/1202.1522