2019 Impact factor 1.347
Condensed Matter and Complex Systems

EPJ B Colloquium - Tensor network theory

Entropy of a 1d MERA: the number of links to cut in order to disconnect the L physical indices in the block form the rest of the system grows logarithmically with L, hence S(L) = O(log L). This is an example of an area-law in holographic space.

Tensor Network (TN) states are a new language, based on entanglement, for quantum many-body states. Román Orús, in a new EPJ B Colloquium, reviews four theoretical developments in TN states for strongly correlated systems.

Specifically, the author considers the effect of symmetries in TN states, fermionic TNs, and the calculation of entanglement Hamiltonians from Projected Entangled Pair States (PEPS). He also examines the relationship between the Multi-scale Entanglement Renormalisation Ansatz (MERA) and the Anti-de Sitter space/Conformal Field Theory (AdS/CFT) or gauge/gravity duality.

The emphasis is on the role of entanglement in the emergence of several physical properties and objects throughout the TN literature, and on some recent results along these lines.

E. Hernandez and H. Rieger
Thank you for the very fruitful and efficient collaboration. It has been a pleasure!!

Paul van Loosdrecht, Guest Editor Topical issue: Excitonic Processes in Condensed Matter, Nanostructured and Molecular Materials, 2013

ISSN (Print Edition): 1434-6028
ISSN (Electronic Edition): 1434-6036

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag