Eur. Phys. J. B (2014) 87: 280
https://doi.org/10.1140/epjb/e2014-50502-9

Colloquium

Advances on tensor network theory: symmetries, fermions, entanglement, and holography

Institute of Physics, Johannes Gutenberg University, 55099 Mainz, Germany

^a e-mail: roman.orus@uni-mainz.de

Received: 24 July 2014
Received in final form: 16 October 2014
Published online: 26 November 2014

Abstract

This is a short review on selected theory developments on tensor network (TN) states for strongly correlated systems. Specifically, we briefly review the effect of symmetries in TN states, fermionic TNs, the calculation of entanglement Hamiltonians from projected entangled pair states (PEPS), and the relation between the multi-scale entanglement renormalization ansatz (MERA) and the AdS/CFT or gauge/gravity duality. We stress the role played by entanglement in the emergence of several physical properties and objects through the TN language. Some recent results along these lines are also discussed.