On the Entanglement Entropy in Gaussian cMERA
arXiv:2104.01551 · doi:10.1002/prop.202100093
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.
arXiv comment18 pages, 1 figure. Some references added in which v2 is the final version published in Fortschritte der Physik. Progress of Physics
References in corpus (21)
- Gauge Theory Correlators from Non-Critical String Theory
- The Large N Limit of Superconformal Field Theories and Supergravity
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Entanglement renormalization
- Quantum corrections to holographic entanglement entropy
- Entanglement Renormalization and Holography
- Entanglement entropy in free quantum field theory
- Entanglement entropy of black holes
- Entanglement entropy: holography and renormalization group
- Entanglement renormalization for quantum fields
- Holographic Geometry of Entanglement Renormalization in Quantum Field Theories
- Beyond Toy Models: Distilling Tensor Networks in Full AdS/CFT
- Entanglement Entropy in Scalar Field Theory
- Entanglement Renormalization for Weakly Interacting Fields
- Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
- 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 Renormalization for Interacting Field Theories
- Entanglement Entropy and Variational Methods: Interacting Scalar Fields
- Entanglement Entropy: Non-Gaussian States and Strong Coupling