This series consists of biweekly seminars on Tensor Networks, ranging from algorithms to their application in condensed matter, quantum gravity, or high energy physics. Each seminar starts with a gentle introduction to the subject under discussion. Everyone is strongly encouraged to participate with questions and comments.
In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework.
I will describe how to define a proper RG flow in the space of
tensor networks, with applications to the evaluation of classical
partition functions, euclidean path integrals, and overlaps of tensor
network states.