Les Houches Lecture Notes on Tensor Networks

TL;DR

Tensor networks offer a powerful framework for understanding complex quantum matter by analyzing entanglement structures, providing computational tools to overcome exponential complexity in many-body systems.

Contribution

This paper provides a concise overview of the conceptual, computational, and mathematical aspects of tensor networks in quantum physics.

Findings

Tensor networks effectively classify topological phases.

They enable efficient simulation of strongly correlated systems.

They reveal the entanglement structure underlying quantum matter.

Abstract

Tensor networks provide a powerful new framework for classifying and simulating correlated and topological phases of quantum matter. Their central premise is that strongly correlated matter can only be understood by studying the underlying entanglement structure and its associated (generalised) symmetries. In essence, tensor networks provide a compressed, holographic description of the complicated vacuum fluctuations in strongly correlated systems, and as such they break down the infamous many-body exponential wall. These lecture notes provide a concise overview of the most important conceptual, computational and mathematical aspects of this theory.