Hologram Horizon Entanglement Entropy/Area Frank Wilczek

"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.

Introduction.—The quantum nature of matter is rarely evident on macroscopic scales, often due to the decoherence of excited states toward classical states. However, for certain states, such as ground or vacuum states, their quantum nature can appear, in principle, on macroscopic scales. One of the most dramatic properties of quantum matter is entanglement and its associated entropy, which, if observed on mesoscopic or macroscopic scales, would be of broad interest. ...
This quantity has appeared in recent investigations in several domains including quantum field theory, condensed matter physics, quantum computing, and black hole physics. It is a mea- sure of one’s ignorance of the full system due to quantum entanglement between the degrees of freedom in the sub- system A and its complement A'. "

Phys. Rev. Lett. 106, 050404 (2011) [4 pages]
Some Calculable Contributions to Entanglement Entropy

Mark P. Hertzberg1,2,* and Frank Wilczek1
1Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2KIPAC and SITP, Stanford University, Stanford, California 94305, USA