Information Geometry of Entanglement Renormalization for free Quantum Fields

TL;DR

This paper explores the geometric structure of entanglement in free quantum fields using the Fisher information metric, revealing invariances and potential insights into spacetime emergence from quantum states.

Contribution

It establishes a connection between entanglement entropy dynamics in tensor networks and a gauge-invariant geometric framework based on information geometry.

Findings

The Fisher information metric describes the geometry of quantum states in tensor networks.

The geometric description remains invariant under gauge transformations.

Results suggest a link between quantum entanglement structure and spacetime emergence.

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.