Condensed Matter Applications of Entanglement Theory

TL;DR

This paper discusses how entanglement theory and tensor network states like MPS and PEPS are used to efficiently describe and analyze quantum many-body systems in condensed matter physics, including their computational limitations.

Contribution

It provides a comprehensive overview of tensor network methods and their applications in condensed matter, highlighting both numerical and analytical approaches.

Findings

Tensor networks efficiently describe many-body quantum states.

Analytical and numerical methods for tensor networks are discussed.

Quantum complexity limits simulation capabilities.

Abstract

These are lecture notes from the 44th IFF Spring School "Quantum Information Processing" in Juelich, discussing applications of entanglement theory in condensed matter. The focus of the notes is on tensor network states, in particular Matrix Product States (MPS) and Projected Entangled Pair States (PEPS), which provide an efficient description of many-body states based on their entanglement structure; both numerical and analytical aspects of tensor networks are being covered. The notes close with a brief introduction to quantum complexity, which allows to assess the limitations to our ability to simulate quantum many-body systems.