On the Entanglement Entropy in Gaussian cMERA

TL;DR

This paper calculates the entanglement entropy in Gaussian cMERA for a free scalar field, linking it to dual AdS geometry and Fisher information, advancing understanding of holographic entanglement in quantum field theories.

Contribution

It establishes a direct relation between cMERA variational parameters, entanglement entropy, and dual AdS geometry, incorporating Fisher information metrics.

Findings

Entanglement entropy expressed via cMERA variational parameters.

Explicit relation between cMERA and AdS geometry through Ryu-Takayanagi formula.

Fisher information metric relates to entanglement entropy and AdS geometry.

Abstract

The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, based on recent formulations of non-Gaussian cMERA circuits, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established.