Abstract
This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.
Acknowledgements
We thank J. Eisert, M. Fannes, J. García-Ripoll, M. Hastings, A. Kitaev, J. Latorre, M. Martín-Delgado, B. Nachtergaele, G. Ortiz, R. Orus, T. Osborne, B. Paredes, D. Pérez-García, M. Plenio, M. Popp, D. Porras, J. Preskill, E. Rico, U. Schollwöck, N. Schuch, C. Schön, E. Solano, G. Vidal, J. von Delft, A. Weichselbaum, R. Werner, S. White, A. Winter, M. Wolf and M. Zwolak for valuable discussions that stimulated the developments of the ideas discussed in this paper.