Abstract
We show that in renormalization group (RG) flow the low-energy states form a code subspace that is approximately protected against the local short-distance errors. To demonstrate how general this connection is, we consider three examples: the classical Ising model in one dimension, free relativistic scalar quantum field theory (QFT) in two spacetime dimensions, and holographic field theories as examples of strongly coupled systems. As a concrete example of real-space RG in QFT, we consider the continuous multiscale renormalization ansatz for massive free fields and show that the low-energy coherent states are approximately protected from the quantum 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.
- Received 16 March 2022
- Accepted 13 October 2022
DOI:https://doi.org/10.1103/PhysRevD.106.105007
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society