Correlation length and unusual corrections to entanglement entropy
We study analytically the corrections to the leading terms in the Rényi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thu...
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| Format: | Article |
| Language: | en_US |
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American Physical Society
2012
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| Online Access: | http://hdl.handle.net/1721.1/74080 |
| _version_ | 1826212446277206016 |
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| author | Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco |
| author_sort | Ercolessi, Elisa |
| collection | MIT |
| description | We study analytically the corrections to the leading terms in the Rényi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Rényi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 conformal field theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path dependent in phase space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain. |
| first_indexed | 2024-09-23T15:21:28Z |
| format | Article |
| id | mit-1721.1/74080 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:21:28Z |
| publishDate | 2012 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/740802022-09-29T14:27:03Z Correlation length and unusual corrections to entanglement entropy Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco Massachusetts Institute of Technology. Department of Physics Franchini, Fabio We study analytically the corrections to the leading terms in the Rényi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Rényi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by a c=1 conformal field theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path dependent in phase space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain. Marie Curie International (Outgoing Fellowship Grant PIOF-PHY-276093) United States. Dept. of Energy. (Contract DE-FG02- 05ER41360) Istituto nazionale di fisica nucleare (INFN) COM4 (Grant FI11) Istituto nazionale di fisica nucleare (INFN) COM4 (Grant NA41) 2012-10-18T16:29:24Z 2012-10-18T16:29:24Z 2012-03 2012-02 Article http://purl.org/eprint/type/JournalArticle 1098-0121 1550-235X http://hdl.handle.net/1721.1/74080 Ercolessi, Elisa et al. “Correlation length and unusual corrections to entanglement entropy.” Physical Review B 85.11 (2012). ©2012 American Physical Society en_US http://dx.doi.org/10.1103/PhysRevB.85.115428 Physical Review B Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society APS |
| spellingShingle | Ercolessi, Elisa Evangelisti, Stefano Franchini, Fabio Ravanini, Francesco Correlation length and unusual corrections to entanglement entropy |
| title | Correlation length and unusual corrections to entanglement entropy |
| title_full | Correlation length and unusual corrections to entanglement entropy |
| title_fullStr | Correlation length and unusual corrections to entanglement entropy |
| title_full_unstemmed | Correlation length and unusual corrections to entanglement entropy |
| title_short | Correlation length and unusual corrections to entanglement entropy |
| title_sort | correlation length and unusual corrections to entanglement entropy |
| url | http://hdl.handle.net/1721.1/74080 |
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