Tensor networks and their application to the classification of phases of matter

Alberto Ruiz de Alarcón

Understanding the entanglement patterns of quantum many-body systems is a central problem in contemporary theoretical physics. In particular, this has led to the introduction of tensor networks, the central object of this talk. We will show how representations of certain algebraic structures give rise to 1-d tensor networks with exotic topological properties and demonstrate their usefulness in understanding topological quantum models, describing renormalization fixed points in 1-d and 2-d, and in classifying quantum phases of matter.