Hyperinvariant multiscale entanglement renormalization ansatz: Approximate holographic error correction codes with power-law correlations

We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when network consists single type also acts as an erasure code, we show it cannot be both locally sustain Motivated by this no-go theorem, desirability local contractibility for efficient ansatz, provide guidelines constructing consisting multiple types tensors correlation. explicit construction one such network, which approximates HaPPY pentagon code in limit where parameters taken to small.