Tensor Network States and Algorithms in the presence of Abelian and non-Abelian Symmetries

Details Tensor Network States and Algorithms in the presence of Abelian and non-Abelian Symmetries Tensor Network States and Algorithms in the presence of Abelian and non-Abelian Symmetries

2012-03-10

arxiv.org/abs/1203.2222v2

Physics

Quantum Physics

PhD Thesis, 182 Pages. Chapters 2,3 and 4 incorporate previously published papers by the author. The material contained in cha

Scientific paper

In this thesis we extend the formalism of tensor network algorithms to incorporate global internal symmetries. We describe how to both numerically protect the symmetry and exploit it for computational gain in tensor network simulations. Our formalism is independent of the details of a specific tensor network decomposition since the symmetry constraints are imposed at the level of individual tensors. Moreover, the formalism can be applied to a wide spectrum of physical symmetries described by any discrete or continuous group that is compact and reducible. We describe in detail the implementation of the conservation of total particle number (U(1) symmetry) and of total angular momentum (SU(2) symmetry). Our formalism can also be readily generalized to incorporate more exotic symmetries such as conservation of total charge in anyonic systems.

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