On the definition of entanglement entropy in lattice gauge theories
A bstract We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert s...
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| Veröffentlicht in: | The journal of high energy physics 2015-06, Vol.2015 (6), p.1-29, Article 187 |
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| container_title | The journal of high energy physics |
| container_volume | 2015 |
| creator | Aoki, Sinya Iritani, Takumi Nozaki, Masahiro Numasawa, Tokiro Shiba, Noburo Tasaki, Hal |
| description | A
bstract
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the
Z
N
gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the
Z
N
gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals. |
| doi_str_mv | 10.1007/JHEP06(2015)187 |
| format | Article |
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bstract
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the
Z
N
gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the
Z
N
gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.</description><identifier>ISSN: 1029-8479</identifier><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP06(2015)187</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Classical and Quantum Gravitation ; Elementary Particles ; Entanglement ; Entropy ; Gages ; Gauge theory ; Gauges ; High energy physics ; Hilbert space ; Invariants ; Lattices ; Physics ; Physics and Astronomy ; Quantum Field Theories ; Quantum Field Theory ; Quantum Physics ; Regular Article - Theoretical Physics ; Relativity Theory ; String Theory</subject><ispartof>The journal of high energy physics, 2015-06, Vol.2015 (6), p.1-29, Article 187</ispartof><rights>The Author(s) 2015</rights><rights>SISSA, Trieste, Italy 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c450t-dc8a97e07f9c3c2a95ea8ffe9a0c976aff65bb39fd59ca128e9a1f9ffd1ac5be3</citedby><cites>FETCH-LOGICAL-c450t-dc8a97e07f9c3c2a95ea8ffe9a0c976aff65bb39fd59ca128e9a1f9ffd1ac5be3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/JHEP06(2015)187$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://doi.org/10.1007/JHEP06(2015)187$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,860,27901,27902,41096,42165,51551</link.rule.ids></links><search><creatorcontrib>Aoki, Sinya</creatorcontrib><creatorcontrib>Iritani, Takumi</creatorcontrib><creatorcontrib>Nozaki, Masahiro</creatorcontrib><creatorcontrib>Numasawa, Tokiro</creatorcontrib><creatorcontrib>Shiba, Noburo</creatorcontrib><creatorcontrib>Tasaki, Hal</creatorcontrib><title>On the definition of entanglement entropy in lattice gauge theories</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the
Z
N
gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the
Z
N
gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.</description><subject>Classical and Quantum Gravitation</subject><subject>Elementary Particles</subject><subject>Entanglement</subject><subject>Entropy</subject><subject>Gages</subject><subject>Gauge theory</subject><subject>Gauges</subject><subject>High energy physics</subject><subject>Hilbert space</subject><subject>Invariants</subject><subject>Lattices</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>String Theory</subject><issn>1029-8479</issn><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNp1kL1PwzAQxS0EEqUws0ZiKUPoOWnieERV-VKlMsBsuc45uErtYidD_3schaFCYrp3ut97Oj1Cbik8UAA2f3tZvUM5y4AW97RiZ2RCIeNptWD8_ERfkqsQdhApymFClhubdF-Y1KiNNZ1xNnE6QdtJ27S4j2JYvDscE2OTVnadUZg0sm9w8DlvMFyTCy3bgDe_c0o-n1Yfy5d0vXl-XT6uU7UooEtrVUnOEJjmKleZ5AXKSmvkEhRnpdS6LLbbnOu64ErSrIoXqrnWNZWq2GI-JbMx9-Ddd4-hE3sTFLattOj6IGgFFRRZxsqI3v1Bd673Nn4nKItUxvNFHqn5SCnvQvCoxcGbvfRHQUEMpYqxVDGUGuNZdMDoCJG0DfqT3H8sP26iehs</recordid><startdate>20150626</startdate><enddate>20150626</enddate><creator>Aoki, Sinya</creator><creator>Iritani, Takumi</creator><creator>Nozaki, Masahiro</creator><creator>Numasawa, Tokiro</creator><creator>Shiba, Noburo</creator><creator>Tasaki, Hal</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PHGZM</scope><scope>PHGZT</scope><scope>PIMPY</scope><scope>PKEHL</scope><scope>PQEST</scope><scope>PQGLB</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20150626</creationdate><title>On the definition of entanglement entropy in lattice gauge theories</title><author>Aoki, Sinya ; 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High Energ. Phys</stitle><date>2015-06-26</date><risdate>2015</risdate><volume>2015</volume><issue>6</issue><spage>1</spage><epage>29</epage><pages>1-29</pages><artnum>187</artnum><issn>1029-8479</issn><eissn>1029-8479</eissn><abstract>A
bstract
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss the issue of gauge invariance of the entanglement entropy. In the
Z
N
gauge theories in arbitrary space dimensions, we show that all the standard properties of the entanglement entropy, e.g. the strong subadditivity, hold in our definition. We study the entanglement entropy for special states, including the topological states for the
Z
N
gauge theories in arbitrary dimensions. We discuss relations of our definition to other proposals.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP06(2015)187</doi><tpages>29</tpages><oa>free_for_read</oa></addata></record> |
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| source | DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; Springer Nature OA Free Journals |
| subjects | Classical and Quantum Gravitation Elementary Particles Entanglement Entropy Gages Gauge theory Gauges High energy physics Hilbert space Invariants Lattices Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory String Theory |
| title | On the definition of entanglement entropy in lattice gauge theories |
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