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

• URL: http://arxiv.org/abs/2103.08631v1
• Date: Mon, 15 Mar 2021 18:12:54 GMT
• Title: Hyper-Invariant MERA: Approximate Holographic Error Correction Codes with Power-Law Correlations
• Authors: ChunJun Cao, Jason Pollack, Yixu Wang
• Abstract summary: We consider a class of holographic tensor networks that are efficiently contractible variational ansatze. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility for an efficient variational ansatz, we provide guidelines for constructing networks consisting of multiple types of tensors that can support power-law correlation. We also provide an explicit construction of one such network, which approximates the holographic HaPPY pentagon code in the limit where variational parameters are taken to be small.

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