Entanglement area law in superfluid $^4$He

TL;DR

This paper presents the first direct numerical evidence of entanglement entropy obeying an area law in a real three-dimensional quantum liquid, superfluid helium-4, linking quantum entanglement to physical properties.

Contribution

It provides the first exact microscopic simulation demonstrating entanglement area law scaling in a real 3D quantum fluid, validating theoretical principles.

Findings

Entanglement entropy in superfluid helium-4 scales with surface area.

Validated the physical origin of the entanglement area law.

Derived an entanglement equation of state depending on superfluid density.

Abstract

Area laws were first discovered by Bekenstein and Hawking, who found that the entropy of a black hole grows proportional to its surface area, and not its volume. Entropy area laws have since become a fundamental part of modern physics, from the holographic principle in quantum gravity to ground state wavefunctions of quantum matter, where entanglement entropy is generically found to obey area law scaling. As no experiments are currently capable of directly probing the entanglement area law in naturally occurring many-body systems, evidence of its existence is based on studies of simplified theories. Using new exact microscopic numerical simulations of superfluid $^4$He, we demonstrate for the first time an area law scaling of entanglement entropy in a real quantum liquid in three dimensions. We validate the fundamental principles underlying its physical origin, and present an "entanglement equation of state" showing how it depends on the density of the superfluid.