A refinement of entanglement entropy and the number of degrees of freedom
Name
Liu_A refinement of.pdf
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3.34 MB
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Author(s)
Liu, Hong
Mezei, Mark Koppany
Date Issued
April 2013
Journal
Journal of High Energy Physics
Publisher
Springer-Verlag
Citation
Liu, Hong, and Mark Mezei. “A Refinement of Entanglement Entropy and the Number of Degrees of Freedom.” J. High Energ. Phys. 2013, no. 4 (April 2013).
Version
Original manuscript
Abstract
We introduce a “renormalized entanglement entropy” which is intrinsically UV finite and is most sensitive to the degrees of freedom at the scale of the size R of the entangled region. We illustrated the power of this construction by showing that the qualitative behavior of the entanglement entropy for a non-Fermi liquid can be obtained by simple dimensional analysis. We argue that the functional dependence of the “renormalized entanglement entropy” on R can be interpreted as describing the renormalization group flow of the entanglement entropy with distance scale. The corresponding quantity for a spherical region in the vacuum, has some particularly interesting properties. For a conformal field theory, it reduces to the previously proposed central charge in all dimensions, and for a general quantum field theory, it interpolates between the central charges of the UV and IR fixed points as R is varied from zero to infinity. We conjecture that in three (spacetime) dimensions, it is always non-negative and monotonic, and provides a measure of the number of degrees of freedom of a system at scale R. In four dimensions, however, we find examples in which it is neither monotonic nor non-negative.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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DOI of Published Version
https://doi.org/10.1007/jhep04(2013)162
