Spread complexity in saddle-dominated scrambling

Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scramb...

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Authors: Huh, K.-B., Jeong, H.-S., Pedraza, J.F.
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2024
Country:España
Institution:Consejo Superior de Investigaciones Científicas (CSIC)
Repository:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/414813
Online Access:http://hdl.handle.net/10261/414813
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85193639553&doi=10.1007%2FJHEP05%282024%29137&partnerID=40&md5=b92ddd3111abca5d1ee899cd7dac08d2
Access Level:Open access
Keyword:AdS-CFT Correspondence
Field Theories in Lower Dimensions
Integrable Field Theories
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spelling Spread complexity in saddle-dominated scramblingHuh, K.-B.Jeong, H.-S.Pedraza, J.F.AdS-CFT CorrespondenceField Theories in Lower DimensionsIntegrable Field TheoriesRecently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scrambling. Specifically, we focus on the Lipkin-Meshkov-Glick model and the inverted harmonic oscillator as representative examples of quantum mechanical systems featuring saddle-dominated scrambling. Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of chaotic systems, displaying a distinctive ramp-peak-slope-plateau pattern. Our results indicate that, although spread complexity serves as a valuable probe, accurately diagnosing true quantum chaos generally necessitates additional physical input. We also explore the relationship between spread complexity, the spectral form factor, and the transition probability within the Krylov space. We provide analytical confirmation of our numerical results, validating the Ehrenfest theorem of complexity and identifying a distinct quadratic behavior in the early-time regime of spread complexity. © The Author(s) 2024.We would like to thank Hugo A. Camargo, Johanna Erdmenger, Viktor Jahnke, Shao-Kai Jian, Keun-Young Kim, Mitsuhiro Nishida, and Zhuo-Yu Xian for valuable discussions and correspondence. KBH is supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (Grant No.NRF-2021R1A2C1006791) and GIST Research Institute (GRI) grant funded by the GIST in 2023. HSJ and JFP are supported by the Spanish MINECO ‘Centro de Excelencia Severo Ochoa’ program under grant SEV-2012-0249, the Comunidad de Madrid ‘Atracción de Talento’ program (ATCAM) grant 2020-T1/TIC-20495, the Spanish Research Agency via grants CEX2020-001007-S and PID2021-123017NB-I00, funded by MCIN/AEI/10.13039/501100011033, and ERDF A way of making Europe.Peer reviewedSpringer NatureMinisterio de Economía y Competitividad (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202620262024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/10261/414813https://www.scopus.com/inward/record.uri?eid=2-s2.0-85193639553&doi=10.1007%2FJHEP05%282024%29137&partnerID=40&md5=b92ddd3111abca5d1ee899cd7dac08d2reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttps://doi.org/10.1007/JHEP05(2024)137Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/4148132026-05-22T06:33:51Z
dc.title.none.fl_str_mv Spread complexity in saddle-dominated scrambling
title Spread complexity in saddle-dominated scrambling
spellingShingle Spread complexity in saddle-dominated scrambling
Huh, K.-B.
AdS-CFT Correspondence
Field Theories in Lower Dimensions
Integrable Field Theories
title_short Spread complexity in saddle-dominated scrambling
title_full Spread complexity in saddle-dominated scrambling
title_fullStr Spread complexity in saddle-dominated scrambling
title_full_unstemmed Spread complexity in saddle-dominated scrambling
title_sort Spread complexity in saddle-dominated scrambling
dc.creator.none.fl_str_mv Huh, K.-B.
Jeong, H.-S.
Pedraza, J.F.
author Huh, K.-B.
author_facet Huh, K.-B.
Jeong, H.-S.
Pedraza, J.F.
author_role author
author2 Jeong, H.-S.
Pedraza, J.F.
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv AdS-CFT Correspondence
Field Theories in Lower Dimensions
Integrable Field Theories
topic AdS-CFT Correspondence
Field Theories in Lower Dimensions
Integrable Field Theories
description Recently, the concept of spread complexity, Krylov complexity for states, has been introduced as a measure of the complexity and chaoticity of quantum systems. In this paper, we study the spread complexity of the thermofield double state within integrable systems that exhibit saddle-dominated scrambling. Specifically, we focus on the Lipkin-Meshkov-Glick model and the inverted harmonic oscillator as representative examples of quantum mechanical systems featuring saddle-dominated scrambling. Applying the Lanczos algorithm, our numerical investigation reveals that the spread complexity in these systems exhibits features reminiscent of chaotic systems, displaying a distinctive ramp-peak-slope-plateau pattern. Our results indicate that, although spread complexity serves as a valuable probe, accurately diagnosing true quantum chaos generally necessitates additional physical input. We also explore the relationship between spread complexity, the spectral form factor, and the transition probability within the Krylov space. We provide analytical confirmation of our numerical results, validating the Ehrenfest theorem of complexity and identifying a distinct quadratic behavior in the early-time regime of spread complexity. © The Author(s) 2024.
publishDate 2024
dc.date.none.fl_str_mv 2024
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/414813
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85193639553&doi=10.1007%2FJHEP05%282024%29137&partnerID=40&md5=b92ddd3111abca5d1ee899cd7dac08d2
url http://hdl.handle.net/10261/414813
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85193639553&doi=10.1007%2FJHEP05%282024%29137&partnerID=40&md5=b92ddd3111abca5d1ee899cd7dac08d2
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://doi.org/10.1007/JHEP05(2024)137
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer Nature
publisher.none.fl_str_mv Springer Nature
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
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