Renormalization group and approximate error correction

• URL: http://arxiv.org/abs/2112.05099v3
• Date: Tue, 26 Apr 2022 13:00:48 GMT
• Title: Renormalization group and approximate error correction
• Abstract summary: We motivate this connection with an example of spin-blocking RG in classical spin models. In holographic RG flows, we study the phase transition in the entanglement wedge of a single region.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In renormalization group (RG) flow, the low energy states form a code subspace that is approximately protected against the local short-distance errors. We motivate this connection with an example of spin-blocking RG in classical spin models. We consider the continuous multi-scale renormalization ansatz (cMERA) for massive free fields as a concrete example of real-space RG in quantum field theory (QFT) and show that the low-energy coherent states are approximately protected from the errors caused by the high-energy localized coherent operators. In holographic RG flows, we study the phase transition in the entanglement wedge of a single region and argue that one needs to define the price and the distance of the code with respect to the reconstructable wedge.

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