The entanglement entropy of a scalar field on the R×S^3 Einstein universe has an infrared contribution from the zero mode with coefficient c_IR = 1/6, distinct from the de Sitter value 1/3.
Some Calculable Contributions to Entanglement Entropy
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Entanglement entropy appears as a central property of quantum systems in broad areas of physics. However, its precise value is often sensitive to unknown microphysics, rendering it incalculable. By considering parametric dependence on correlation length, we extract finite, calculable contributions to the entanglement entropy for a scalar field between the interior and exterior of a spatial domain of arbitrary shape. The leading term is proportional to the area of the dividing boundary; we also extract finite subleading contributions for a field defined in the bulk interior of a waveguide in 3+1 dimensions, including terms proportional to the waveguide's cross-sectional geometry; its area, perimeter length, and integrated curvature. We also consider related quantities at criticality and suggest a class of systems for which these contributions might be measurable.
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Entanglement on a Sphere
The entanglement entropy of a scalar field on the R×S^3 Einstein universe has an infrared contribution from the zero mode with coefficient c_IR = 1/6, distinct from the de Sitter value 1/3.