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Particles and Fields

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.

L. Baudis, G. Dissertori, K. Skenderis and D. Zeppenfeld
We are grateful to the Editor, to the Referee for careful reading of the manuscript, for the interesting and useful remarks, which allow us to improve the text and clarify some of the results.

Evgenij Martynov (Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine) and Basarab Nicolescu (Babes-Bolyai University, Cluj-Napoca, Romania)

ISSN: 1434-6044 (Print Edition)
ISSN: 1434-6052 (Electronic Edition)

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