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

TL;DR

This thesis develops a general tensor network formalism that incorporates and exploits global internal symmetries, such as U(1) and SU(2), for more efficient and symmetry-preserving simulations in quantum many-body physics.

Contribution

It introduces a symmetry-agnostic tensor network framework that can handle a wide range of symmetries, including Abelian, non-Abelian, and exotic symmetries, at the tensor level.

Findings

Formalism preserves symmetries numerically.

Exploits symmetries for computational efficiency.

Applicable to various physical symmetry groups.

Abstract

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.