A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States

TL;DR

This paper provides a practical, accessible introduction to tensor network methods, focusing on Matrix Product States and Projected Entangled Pair States, emphasizing their numerical applications in quantum lattice systems.

Contribution

It offers a non-technical overview of tensor networks, explaining key concepts and numerical techniques for MPS and PEPS, suitable for newcomers to the field.

Findings

Clarifies the concept of tensor networks and their importance.

Describes numerical methods for 1D and 2D quantum systems.

Provides illustrative examples and foundational knowledge.

Abstract

This is a partly non-technical introduction to selected topics on tensor network methods, based on several lectures and introductory seminars given on the subject. It should be a good place for newcomers to get familiarized with some of the key ideas in the field, specially regarding the numerics. After a very general introduction we motivate the concept of tensor network and provide several examples. We then move on to explain some basics about Matrix Product States (MPS) and Projected Entangled Pair States (PEPS). Selected details on some of the associated numerical methods for 1d and 2d quantum lattice systems are also discussed.