A refinement of entanglement entropy and the number of degrees of freedom
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 f...
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| Format: | Article |
| Language: | en_US |
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Springer-Verlag
2014
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| Online Access: | http://hdl.handle.net/1721.1/88521 https://orcid.org/0000-0002-4911-3183 |
| _version_ | 1811074669974913024 |
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| author | Liu, Hong Mezei, Mark Koppany |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Liu, Hong Mezei, Mark Koppany |
| author_sort | Liu, Hong |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:53:29Z |
| format | Article |
| id | mit-1721.1/88521 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:53:29Z |
| publishDate | 2014 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/885212022-09-30T17:28:57Z A refinement of entanglement entropy and the number of degrees of freedom Liu, Hong Mezei, Mark Koppany Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Laboratory for Nuclear Science Liu, Hong Mezei, Mark Koppany 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. United States. Dept. of Energy (Cooperative Research Agreement DE-FG0205ER41360) 2014-07-30T13:03:09Z 2014-07-30T13:03:09Z 2013-04 2013-03 Article http://purl.org/eprint/type/JournalArticle 1029-8479 1126-6708 http://hdl.handle.net/1721.1/88521 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). https://orcid.org/0000-0002-4911-3183 en_US http://dx.doi.org/10.1007/jhep04(2013)162 Journal of High Energy Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Springer-Verlag arXiv |
| spellingShingle | Liu, Hong Mezei, Mark Koppany A refinement of entanglement entropy and the number of degrees of freedom |
| title | A refinement of entanglement entropy and the number of degrees of freedom |
| title_full | A refinement of entanglement entropy and the number of degrees of freedom |
| title_fullStr | A refinement of entanglement entropy and the number of degrees of freedom |
| title_full_unstemmed | A refinement of entanglement entropy and the number of degrees of freedom |
| title_short | A refinement of entanglement entropy and the number of degrees of freedom |
| title_sort | refinement of entanglement entropy and the number of degrees of freedom |
| url | http://hdl.handle.net/1721.1/88521 https://orcid.org/0000-0002-4911-3183 |
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