https://arxiv.org/abs/0910.1130 Renormalization and tensor product states in spin chains and lattices J. I. Cirac, F. Verstraete (Submitted on 6 Oct 2009) We review different descriptions of many--body quantum systems in terms of tensor product states. We introduce several families of such states in terms of known renormalization procedures, and show that they naturally arise in that context. We concentrate on Matrix Product States, T
