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 ( C P ) against the action of greedy algorithm. For given tensor constraints, a C P 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 C P tensor chain. Four classes of tensor networks with different properties of entanglement are discussed. Thanks to tensor constraints and C P , the correlation function is reduced into a bracket of matrix production state and the result agrees with the one in conformal field theory.
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