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EPJ ST - Special Topics
Special Topics

EPJ B Colloquium - Tensor network theory

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Published on 01 December 2014
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.

Román Orús (2014),
Advances on tensor network theory: symmetries, fermions, entanglement, and holography,
European Physical Journal B, DOI: 10.1140/epjb/e2014-50502-9

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Managing Editors
Sandrine Karpe and Vijala Kiruvanayagam (EDP Sciences) and Sabine Lehr (Springer-Verlag)
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Dear Isabelle,
Many thanks for all the hard work. Many thanks indeed!

Peter M.A. Sloot, University of Amsterdam, The Netherlands
Editor EPJ Special Topics 222/6, 2013

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ISSN: 1951-6355 (Print Edition)
ISSN: 1951-6401 (Electronic Edition)

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