Entanglement renormalization for quantum fields

TL;DR

This work introduces the continuum multiscale entanglement renormalization ansatz (cMERA) to realize real-space renormalization group flows in quantum field theories. By coupling a local entangler K(s) to a dilation generator L, cMERA provides a translation-invariant, variational framework with built-in UV and IR cutoffs, bridging MERA concepts to continuum QFTs. The authors derive an operator RG flow, argue for an entropy/area law within this framework, and demonstrate a Gaussian cMERA representation for ground states of a local quadratic bosonic model, including the critical limit. The approach promises applications to strongly interacting QFTs and suggests deep links to holography, such as AdS/CFT, via entanglement-driven renormalization.

Abstract

It is shown how to construct renormalization group flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space. This is achieved by generalizing the multiscale entanglement renormalization ansatz to continuum theories. The variational class of wavefunctions arising from this RG flow are translation invariant and exhibit an entropy-area law. We illustrate the construction for a free non-relativistic boson model, and argue that the full power of the construction should emerge in the case of interacting theories.