Information Geometry of Entanglement Renormalization for free Quantum Fields

Abstract

We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.

18 pages. 1 eps figure. References added. Some comments added

References in corpus (6)

• Gravitation from Entanglement in Holographic CFTs
• Continuous Matrix Product States for Quantum Fields
• Surface/State Correspondence as a Generalized Holography
• cMERA as Surface/State Correspondence in AdS/CFT
• Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
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• The Large $N$ Limit of icMERA and Holography
• Tensor Renormalization Group for interacting quantum fields
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Entanglement renormalization for quantum fields with boundaries and defects