Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems

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.

Keywords:

• matrix product states
• projected entangled pair states
• numerical renormalization group
• density matrix renormalization group
• entanglement
• quantum spin chains
• strongly correlated quantum systems

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.