1203.2222 (Sukhwinder Singh)

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

Sukhwinder Singh

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 compact discrete or continuous group. We describe in detail the implementation of the conservation of total particle number (U(1) symmetry) and of total angular momentum (SU(2) symmetry). The formalism can also be readily generalized to the case of more exotic symmetries such as conservation of total charge in anyonic systems.

View original: http://arxiv.org/abs/1203.2222