Crosscap States in Integrable Field Theories and Spin Chains
We study crosscap states in integrable field theories and spin chains in 1 + 1 dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the crosscap entropy , i.e. the overlap for the g...
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| Veröffentlicht in: | Journal of statistical physics 2022-06, Vol.187 (3), Article 30 |
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| creator | Caetano, João Komatsu, Shota |
| description | We study crosscap states in integrable field theories and spin chains in
1
+
1
dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the
crosscap entropy
, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov’s staircase model to flows between
D
-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection. |
| doi_str_mv | 10.1007/s10955-022-02914-6 |
| format | Article |
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1
+
1
dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the
crosscap entropy
, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov’s staircase model to flows between
D
-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.</description><identifier>ISSN: 0022-4715</identifier><identifier>EISSN: 1572-9613</identifier><identifier>DOI: 10.1007/s10955-022-02914-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Chains ; Eigenvectors ; Entropy ; Initial conditions ; Mathematical and Computational Physics ; Physical Chemistry ; Physics ; Physics and Astronomy ; Quantum Physics ; Statistical Physics and Dynamical Systems ; Theoretical</subject><ispartof>Journal of statistical physics, 2022-06, Vol.187 (3), Article 30</ispartof><rights>The Author(s) 2022</rights><rights>COPYRIGHT 2022 Springer</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c438t-ea5638627c8828a0e48ac53714f5d3bbb0b5de6cde1861322bd83c22a5da3c0e3</citedby><cites>FETCH-LOGICAL-c438t-ea5638627c8828a0e48ac53714f5d3bbb0b5de6cde1861322bd83c22a5da3c0e3</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/s10955-022-02914-6$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10955-022-02914-6$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Caetano, João</creatorcontrib><creatorcontrib>Komatsu, Shota</creatorcontrib><title>Crosscap States in Integrable Field Theories and Spin Chains</title><title>Journal of statistical physics</title><addtitle>J Stat Phys</addtitle><description>We study crosscap states in integrable field theories and spin chains in
1
+
1
dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the
crosscap entropy
, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov’s staircase model to flows between
D
-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.</description><subject>Chains</subject><subject>Eigenvectors</subject><subject>Entropy</subject><subject>Initial conditions</subject><subject>Mathematical and Computational Physics</subject><subject>Physical Chemistry</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Physics</subject><subject>Statistical Physics and Dynamical Systems</subject><subject>Theoretical</subject><issn>0022-4715</issn><issn>1572-9613</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9kM9LwzAUx4MoOKf_gKeC52p-NGkKXkZxOhh42DyHNHndMrq0Jt3B_97MCt4khEDe9_Pe44PQPcGPBOPyKRJccZ5jStOtSJGLCzQjvKR5JQi7RDN8LhUl4dfoJsYDxriSFZ-h5zr0MRo9ZJtRjxAz57OVH2EXdNNBtnTQ2Wy7hz64VNTeZpshReq9dj7eoqtWdxHuft85-li-bOu3fP3-uqoX69wUTI45aC6YFLQ0UlKpMRRSG85KUrTcsqZpcMMtCGOByLQtpY2VzFCqudXMYGBz9DD1HUL_eYI4qkN_Cj6NVFRwxgVlUqbU45Ta6Q6U820_Bm3SsXB0pvfQuvS_KDFhjMqySgCdAHN2EKBVQ3BHHb4UweqsVU1aVXKnfrQqkSA2QTGF_Q7C3y7_UN9q4njY</recordid><startdate>20220601</startdate><enddate>20220601</enddate><creator>Caetano, João</creator><creator>Komatsu, Shota</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20220601</creationdate><title>Crosscap States in Integrable Field Theories and Spin Chains</title><author>Caetano, João ; Komatsu, Shota</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c438t-ea5638627c8828a0e48ac53714f5d3bbb0b5de6cde1861322bd83c22a5da3c0e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Chains</topic><topic>Eigenvectors</topic><topic>Entropy</topic><topic>Initial conditions</topic><topic>Mathematical and Computational Physics</topic><topic>Physical Chemistry</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Physics</topic><topic>Statistical Physics and Dynamical Systems</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Caetano, João</creatorcontrib><creatorcontrib>Komatsu, Shota</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Journal of statistical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Caetano, João</au><au>Komatsu, Shota</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Crosscap States in Integrable Field Theories and Spin Chains</atitle><jtitle>Journal of statistical physics</jtitle><stitle>J Stat Phys</stitle><date>2022-06-01</date><risdate>2022</risdate><volume>187</volume><issue>3</issue><artnum>30</artnum><issn>0022-4715</issn><eissn>1572-9613</eissn><abstract>We study crosscap states in integrable field theories and spin chains in
1
+
1
dimensions. We derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. We then compute the
crosscap entropy
, i.e. the overlap for the ground state, in some examples. In the examples we analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. We next introduce crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. These states are long-range entangled and their entanglement entropy grows linearly until the size of the subregion reaches half the system size. This property is reminiscent of pure-state black holes in holography and makes them interesting for use as initial conditions of quantum quench. As side results, we propose a generalization of Zamolodchikov’s staircase model to flows between
D
-series minimal models, and discuss the relation to fermionic minimal models and the GSO projection.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10955-022-02914-6</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Chains Eigenvectors Entropy Initial conditions Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical |
| title | Crosscap States in Integrable Field Theories and Spin Chains |
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