On the Entanglement Entropy in Gaussian cMERA

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.

18 pages, 1 figure. Some references added in which v2 is the final version published in Fortschritte der Physik. Progress of Physics

References in corpus (5)

• Entanglement Entropy in Scalar Field Theory
• Towards Spacetime Entanglement Entropy for Interacting Theories
• Entanglement and correlations in the continuous multi-scale entanglement renormalization ansatz
• Non-Gaussian Entanglement Renormalization for Quantum Fields
• Entanglement Entropy: Non-Gaussian States and Strong Coupling

Cited by in corpus (2)

• The Large $N$ Limit of icMERA and Holography
• Entanglement Renormalization of a $T\bar{T}$-deformed CFT