Entanglement renormalization for quantum fields

TL;DR

This paper introduces a real-space renormalization group method for quantum field theories using a continuum extension of entanglement renormalization, demonstrating its effectiveness on a free boson model and its potential for interacting theories.

Contribution

It generalizes the multiscale entanglement renormalization ansatz to continuum quantum field theories, enabling real-space RG flows and translation-invariant wavefunctions.

Findings

Constructed RG flows in real space for quantum fields.

Wavefunctions obey an entropy-area law.

Illustrated method on a free boson model.

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.