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We consider a class of holographic tensor networks that are efficientlycontractible variational ansatze, manifestly (approximate) quantum errorcorrection codes, and can support power-law correlation functions. In the casewhen the network consists of a single type of tensor that also acts as anerasure correction code, we show that it cannot be both locally contractibleand sustain power-law correlation functions. Motivated by this no-go theorem,and the desirability of local contractibility for an efficient variationalansatz, we provide guidelines for constructing networks consisting of multipletypes of tensors that can support power-law correlation. We also provide anexplicit construction of one such network, which approximates the holographicHaPPY pentagon code in the limit where variational parameters are taken to besmall.

Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations