A sort of planar tensor network with tensor constraints is investigated as a model for holography. We study the greedy algorithm generated by tensor constraints and propose the notion of critical protection ($CP$) against the action of greedy algorithm. For given tensor constraints, a $CP$ tensor chain can be defined. We further find that the ability of quantum error correction (QEC), the non-flatness of entanglement spectrum (ES) and the correlation function can be quantitatively evaluated by the geometric structure of $CP$ tensor chain. Four classes of tensor networks with different properties of entanglement are discussed. Thanks to tensor constraints and $CP$, the correlation function is reduced into a bracket of matrix production state and the result agrees with the one in conformal field theory.

• Received 7 August 2018

DOI:https://doi.org/10.1103/PhysRevD.99.026008

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Published by the American Physical Society