Entanglement Entropy and Berezin–Toeplitz Operators
We consider Berezin–Toeplitz operators on compact Kähler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a conseq...
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| Veröffentlicht in: | Communications in mathematical physics 2020-05, Vol.376 (1), p.521-554 |
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| container_title | Communications in mathematical physics |
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| creator | Charles, Laurent Estienne, Benoit |
| description | We consider Berezin–Toeplitz operators on compact Kähler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a consequence, we deduce the area law for the entanglement entropy of integer quantum Hall states. Another application is for the determinantal processes with correlation kernel the Bergman kernels of a positive line bundle: we prove that the number of points in a smooth domain is asymptotically normal. |
| doi_str_mv | 10.1007/s00220-019-03625-y |
| format | Article |
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Math. Phys</addtitle><description>We consider Berezin–Toeplitz operators on compact Kähler manifolds whose symbols are characteristic functions. When the support of the characteristic function has a smooth boundary, we prove a two-term Weyl law, the second term being proportional to the Riemannian volume of the boundary. As a consequence, we deduce the area law for the entanglement entropy of integer quantum Hall states. Another application is for the determinantal processes with correlation kernel the Bergman kernels of a positive line bundle: we prove that the number of points in a smooth domain is asymptotically normal.</description><subject>Characteristic functions</subject><subject>Classical and Quantum Gravitation</subject><subject>Complex Systems</subject><subject>Condensed Matter</subject><subject>Entanglement</subject><subject>Entropy</subject><subject>Kernels</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Physics</subject><subject>Mathematics</subject><subject>Mesoscopic Systems and Quantum Hall Effect</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Probability</subject><subject>Quantum Physics</subject><subject>Relativity Theory</subject><subject>Smooth boundaries</subject><subject>Spectral Theory</subject><subject>Theoretical</subject><issn>0010-3616</issn><issn>1432-0916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAQhi0EEqXwAkyRmBgMZzt24rFUQJEqdSmzZbtOSZUmwU6R0ol34A15ElyCYGM63en7f50-hC4J3BCA7DYAUAoYiMTABOW4P0IjkjKKQRJxjEYABDATRJyisxA2ACCpECPE7-tO1-vKbV3dJXHxTdsnul4ld867fVl_vn8sG9dWZbdPFq3zumt8OEcnha6Cu_iZY_T8cL-czvB88fg0ncyxZZx1mOa5ME6mhDHJuLDC2sxQksWjKawxGZc6NzloxgpIM25WJs8zYIykxlqRsjG6HnpfdKVaX26171WjSzWbzNXhBikAFzx9I5G9GtjWN687Fzq1aXa-ju8pymROKWcSIkUHyvomBO-K31oC6qBSDSpVVKm-Vao-htgQChGu187_Vf-T-gJKUnY9</recordid><startdate>20200501</startdate><enddate>20200501</enddate><creator>Charles, Laurent</creator><creator>Estienne, Benoit</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><orcidid>https://orcid.org/0000-0002-3430-012X</orcidid><orcidid>https://orcid.org/0000-0003-2316-9661</orcidid></search><sort><creationdate>20200501</creationdate><title>Entanglement Entropy and Berezin–Toeplitz Operators</title><author>Charles, Laurent ; Estienne, Benoit</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-2886be941339356c6cc7b2176bebfcbb759a8b80a33f0475bdb88703314bcc643</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Characteristic functions</topic><topic>Classical and Quantum Gravitation</topic><topic>Complex Systems</topic><topic>Condensed Matter</topic><topic>Entanglement</topic><topic>Entropy</topic><topic>Kernels</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Physics</topic><topic>Mathematics</topic><topic>Mesoscopic Systems and Quantum Hall Effect</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Probability</topic><topic>Quantum Physics</topic><topic>Relativity Theory</topic><topic>Smooth boundaries</topic><topic>Spectral Theory</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Charles, Laurent</creatorcontrib><creatorcontrib>Estienne, Benoit</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Communications in mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Charles, Laurent</au><au>Estienne, Benoit</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Entanglement Entropy and Berezin–Toeplitz Operators</atitle><jtitle>Communications in mathematical physics</jtitle><stitle>Commun. 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| language | eng |
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| subjects | Characteristic functions Classical and Quantum Gravitation Complex Systems Condensed Matter Entanglement Entropy Kernels Mathematical and Computational Physics Mathematical Physics Mathematics Mesoscopic Systems and Quantum Hall Effect Operators (mathematics) Physics Physics and Astronomy Probability Quantum Physics Relativity Theory Smooth boundaries Spectral Theory Theoretical |
| title | Entanglement Entropy and Berezin–Toeplitz Operators |
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