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A refinement of entanglement entropy and the number of degrees of freedom

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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.

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  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, U.S.A.

    Hong Liu & Márk Mezei

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  1. Hong Liu
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Liu, H., Mezei, M. A refinement of entanglement entropy and the number of degrees of freedom. J. High Energ. Phys. 2013, 162 (2013). https://doi.org/10.1007/JHEP04(2013)162

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