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Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain
The transverse field in the quantum Ising chain is linearly ramped from the para- to the ferromagnetic phase across the quantum critical point at a rate characterized by a quench time τQ. We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a s...
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Published in: | Physical review. B 2021-08, Vol.104 (7), Article 075448 |
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description | The transverse field in the quantum Ising chain is linearly ramped from the para- to the ferromagnetic phase across the quantum critical point at a rate characterized by a quench time τQ. We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a sum of two terms: a negative (antibunching) Gaussian that depends on the Kibble-Zurek correlation length only and a positive term that depends on a second longer scale of length. The second length is made longer by dephasing of the state excited near the critical point during the following ramp across the ferromagnetic phase. This interpretation is corroborated by considering a linear ramp that is halted in the ferromagnetic phase for a finite waiting time and then continued at the same rate as before the halt. The extra time available for dephasing increases the second scale of length that asymptotically grows linearly with the waiting time. The dephasing also suppresses magnitude of the second term, making it negligible for waiting times much longer than τQ. The same dephasing can be obtained with a smooth ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing, we also obtain higher order kink correlators and the ferromagnetic correlation function. |
doi_str_mv | 10.1103/PhysRevB.104.075448 |
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We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a sum of two terms: a negative (antibunching) Gaussian that depends on the Kibble-Zurek correlation length only and a positive term that depends on a second longer scale of length. The second length is made longer by dephasing of the state excited near the critical point during the following ramp across the ferromagnetic phase. This interpretation is corroborated by considering a linear ramp that is halted in the ferromagnetic phase for a finite waiting time and then continued at the same rate as before the halt. The extra time available for dephasing increases the second scale of length that asymptotically grows linearly with the waiting time. The dephasing also suppresses magnitude of the second term, making it negligible for waiting times much longer than τQ. The same dephasing can be obtained with a smooth ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing, we also obtain higher order kink correlators and the ferromagnetic correlation function.</description><identifier>ISSN: 2469-9950</identifier><identifier>EISSN: 2469-9969</identifier><identifier>DOI: 10.1103/PhysRevB.104.075448</identifier><language>eng</language><publisher>College Park: American Physical Society</publisher><subject>Chains ; Correlation ; Correlators ; Critical point ; Ferromagnetic phases ; Ferromagnetism ; Ising model</subject><ispartof>Physical review. 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The dephasing also suppresses magnitude of the second term, making it negligible for waiting times much longer than τQ. The same dephasing can be obtained with a smooth ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing, we also obtain higher order kink correlators and the ferromagnetic correlation function.</description><subject>Chains</subject><subject>Correlation</subject><subject>Correlators</subject><subject>Critical point</subject><subject>Ferromagnetic phases</subject><subject>Ferromagnetism</subject><subject>Ising model</subject><issn>2469-9950</issn><issn>2469-9969</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNo9UMtOwzAQtBBIVKVfwMUS55R17Ng1N6igVFTiIbjAwbKNQ9I2TrETpP49RgEuuzuj2dnVIHRKYEoI0POHah-f3NfVlACbgigYmx2gUc64zKTk8vB_LuAYTWJcAwDhIAXIEXp77LXv-gbf1cZsXfbaB7fBjbOV9nVsLhLvN9i2Ibit7urWR6zLzgWs8WfvvK1w7XFXuYQGn2Ws_QdO67U_QUel3kY3-e1j9HJz_Ty_zVb3i-X8cpVZymiXWUOILgVwYqmRupgVnJZ5bsW7FKY0glNBwBAnRRKZBAouuZ1pkafKtKVjdDb47kKbnoqdWrd98OmkygsBOSNEQFLRQWVDG2NwpdqFutFhrwionyDVX5CJYGoIkn4Dvy9nxw</recordid><startdate>20210830</startdate><enddate>20210830</enddate><creator>Nowak, Radosław J.</creator><creator>Dziarmaga, Jacek</creator><general>American Physical Society</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SR</scope><scope>7U5</scope><scope>8BQ</scope><scope>8FD</scope><scope>H8D</scope><scope>JG9</scope><scope>L7M</scope><orcidid>https://orcid.org/0000-0002-7361-4252</orcidid></search><sort><creationdate>20210830</creationdate><title>Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain</title><author>Nowak, Radosław J. ; Dziarmaga, Jacek</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c343t-cb11af7061c3b9a58563f22c7d97bfb763710b1e97f70b3715696c8a726c84ac3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Chains</topic><topic>Correlation</topic><topic>Correlators</topic><topic>Critical point</topic><topic>Ferromagnetic phases</topic><topic>Ferromagnetism</topic><topic>Ising model</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nowak, Radosław J.</creatorcontrib><creatorcontrib>Dziarmaga, Jacek</creatorcontrib><collection>CrossRef</collection><collection>Engineered Materials Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>METADEX</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Materials Research Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Physical review. B</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nowak, Radosław J.</au><au>Dziarmaga, Jacek</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain</atitle><jtitle>Physical review. B</jtitle><date>2021-08-30</date><risdate>2021</risdate><volume>104</volume><issue>7</issue><artnum>075448</artnum><issn>2469-9950</issn><eissn>2469-9969</eissn><abstract>The transverse field in the quantum Ising chain is linearly ramped from the para- to the ferromagnetic phase across the quantum critical point at a rate characterized by a quench time τQ. We calculate a connected kink-kink correlator in the final state at zero transverse field. The correlator is a sum of two terms: a negative (antibunching) Gaussian that depends on the Kibble-Zurek correlation length only and a positive term that depends on a second longer scale of length. The second length is made longer by dephasing of the state excited near the critical point during the following ramp across the ferromagnetic phase. This interpretation is corroborated by considering a linear ramp that is halted in the ferromagnetic phase for a finite waiting time and then continued at the same rate as before the halt. The extra time available for dephasing increases the second scale of length that asymptotically grows linearly with the waiting time. The dephasing also suppresses magnitude of the second term, making it negligible for waiting times much longer than τQ. The same dephasing can be obtained with a smooth ramp that slows down in the ferromagnetic phase. Assuming sufficient dephasing, we also obtain higher order kink correlators and the ferromagnetic correlation function.</abstract><cop>College Park</cop><pub>American Physical Society</pub><doi>10.1103/PhysRevB.104.075448</doi><orcidid>https://orcid.org/0000-0002-7361-4252</orcidid></addata></record> |
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subjects | Chains Correlation Correlators Critical point Ferromagnetic phases Ferromagnetism Ising model |
title | Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain |
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