Renormalization and tensor product states in spin chains and lattices

TL;DR

This paper reviews tensor product state methods for many-body quantum systems, focusing on their properties and applications in spin chains and lattices, emphasizing their connection to renormalization procedures.

Contribution

It introduces and compares various tensor network states derived from renormalization techniques, clarifying their roles in modeling quantum many-body systems.

Findings

Matrix Product States effectively describe 1D systems.

Tree Tensor States capture hierarchical entanglement.

Multiscale Entanglement Renormalization Ansatz models scale-invariant systems.

Abstract

We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context. We concentrate on Matrix Product States, Tree Tensor States, Multiscale Entanglement Renormalization Ansatz, and Projected Entangled Pair States. We highlight some of their properties, and show how they can be used to describe a variety of systems.