Exact Renormalization of Wave Functionals yields Continuous MERA

TL;DR

This paper develops an exact renormalization framework for wavefunctionals, leading to a class of continuous entanglement renormalization networks like cMERA, which can be derived from a fundamental RG principle and may extend beyond free fields.

Contribution

It introduces a generalized wavefunctional ERG scheme that derives cMERA from a microscopic principle, enabling modifications of dispersion relations and deeper understanding of entanglement in continuum theories.

Findings

Derived cMERA from a fundamental RG principle.

Allowed modifications of dispersion relations affecting entanglement.

Provided a pathway to extend cMERA beyond free theories.

Abstract

The exact renormalization group (ERG) is a powerful tool for understanding the formal properties of field theories. By adapting generalized ERG schemes to the flow of wavefunctionals, we obtain a large class of continuous unitary networks, a special case of which includes a class of Gaussian continuous Multi-scale Renormalization Ansatzes (cMERAs). The novel feature of these generalized wavefunctional ERG schemes is allowing for modifications of the dispersion relation, which drastically changes the entanglement structure of the ultraviolet states. Through our construction, we demonstrate that cMERA can be derived from a more fundamental "microscopic" principle, which amounts to the usual RG principle of path integral independence, suitably adapted to quantum states of the field theory. The establishment of such a principle may provide a path forward for exploring cMERA beyond the free field regime, and for understanding the nature of entanglement renormalization intrinsically in the continuum.