Time dependence of entanglement entropy on the fuzzy sphere

Abstract

We numerically study the behaviour of entanglement entropy for a free scalar field on the noncommutative ("fuzzy") sphere after a mass quench. It is known that the entanglement entropy before a quench violates the usual area law due to the non-local nature of the theory. By comparing our results to the ordinary sphere, we find results that, despite this non-locality, are compatible with entanglement being spread by ballistic propagation of entangled quasi-particles at a speed no greater than the speed of light. However, we also find that, when the pre-quench mass is much larger than the inverse of the short-distance cutoff of the fuzzy sphere (a regime with no commutative analogue), the entanglement entropy spreads faster than allowed by a local model.

1+14 pages, 8 figures v2: References added, matches published version

References in corpus (4)

• A-branes and Noncommutative Geometry
• Entanglement Entropy on Fuzzy Spaces
• On holographic entanglement entropy of non-local field theories
• Mutual information on the fuzzy sphere

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• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Entanglement entropy on a fuzzy sphere with a UV cutoff
• Green's Function Approach to Entanglement Entropy on Lattices and Fuzzy Spaces
• Recent developments in the holographic description of quantum chaos