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.

Exact Renormalization of Wave Functionals yields continuous MERA

“…It would also be interesting to further explore the connection between renormalization and error correction as put forth in [17]. There, the RG flows are viewed as an encoding channel for a particular set of low-energy states.…”