A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom

We present an overview of the key ideas and skills necessary to begin implementing tensor network methods numerically, which is intended to facilitate the practical application of tensor network methods for researchers that are already versed with their theoretical foundations. These skills include an introduction to the contraction of tensor networks, to optimal tensor decompositions, and to the manipulation of gauge degrees of freedom in tensor networks. The topics presented are of key importance to many common tensor network algorithms such as DMRG, TEBD, TRG, PEPS, and MERA.