Renormalization group and approximate error correction
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.
Cite
@article{arxiv.2112.05099,
title = {Renormalization group and approximate error correction},
author = {Keiichiro Furuya and Nima Lashkari and Mudassir Moosa},
journal= {arXiv preprint arXiv:2112.05099},
year = {2022}
}