Tensor networks for quantum matter: basics, news and prospects
Tensor network states have established themselves as the natural language based on entanglement to describe and numerically simulate quantum many-body systems. In this talk I will first provide an introduction to what tensor network states are, as well as to some of their related numerical methods. An overall perspective on the field will also be provided. Then, I will review recent progress on this topic conducted in my group. In particular, I will focus on the study of (i) 2d topological order, and (ii) Kagome Heisenberg antiferromagnets on a field, but other relevant developments will also be briefly discussed. Finally, I will discuss future research directions including the role of tensor networks in AdS/CFT, lattice gauge theories, many-body localization, and other recent ideas.