Krylov complexity as an order parameter for quantum chaotic-integrable transitions
Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are a prerogative of quantum chaotic systems and how they relate to more standard probes, such as spectral statistics or out-of-time-order correla...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.023028 |
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| author | Matteo Baggioli Kyoung-Bum Huh Hyun-Sik Jeong Keun-Young Kim Juan F. Pedraza |
| author_facet | Matteo Baggioli Kyoung-Bum Huh Hyun-Sik Jeong Keun-Young Kim Juan F. Pedraza |
| author_sort | Matteo Baggioli |
| collection | DOAJ |
| description | Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are a prerogative of quantum chaotic systems and how they relate to more standard probes, such as spectral statistics or out-of-time-order correlators (OTOCs), remain open questions. Recent insights have revealed that in quantum chaotic systems Krylov state complexity exhibits a distinct peak during time evolution before settling into a well-understood late-time plateau. In this work we propose that this Krylov complexity peak (KCP) is a hallmark of quantum chaotic systems and suggest that its height could serve as an order parameter for quantum chaos. We demonstrate that the KCP effectively identifies chaotic-integrable transitions in two representative quantum-mechanical models at both infinite and finite temperature: the mass-deformed Sachdev-Ye-Kitaev model and the sparse Sachdev-Ye-Kitaev model. Our findings align with established results from spectral statistics and OTOCs while introducing an operator-independent diagnostic for quantum chaos, offering more universal insights and a deeper understanding of the general properties of quantum chaotic systems. |
| format | Article |
| id | doaj-art-c97b2d0ba6e2425daa098c76fa825e44 |
| institution | DOAJ |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-c97b2d0ba6e2425daa098c76fa825e442025-08-20T03:17:59ZengAmerican Physical SocietyPhysical Review Research2643-15642025-04-017202302810.1103/PhysRevResearch.7.023028Krylov complexity as an order parameter for quantum chaotic-integrable transitionsMatteo BaggioliKyoung-Bum HuhHyun-Sik JeongKeun-Young KimJuan F. PedrazaKrylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are a prerogative of quantum chaotic systems and how they relate to more standard probes, such as spectral statistics or out-of-time-order correlators (OTOCs), remain open questions. Recent insights have revealed that in quantum chaotic systems Krylov state complexity exhibits a distinct peak during time evolution before settling into a well-understood late-time plateau. In this work we propose that this Krylov complexity peak (KCP) is a hallmark of quantum chaotic systems and suggest that its height could serve as an order parameter for quantum chaos. We demonstrate that the KCP effectively identifies chaotic-integrable transitions in two representative quantum-mechanical models at both infinite and finite temperature: the mass-deformed Sachdev-Ye-Kitaev model and the sparse Sachdev-Ye-Kitaev model. Our findings align with established results from spectral statistics and OTOCs while introducing an operator-independent diagnostic for quantum chaos, offering more universal insights and a deeper understanding of the general properties of quantum chaotic systems.http://doi.org/10.1103/PhysRevResearch.7.023028 |
| spellingShingle | Matteo Baggioli Kyoung-Bum Huh Hyun-Sik Jeong Keun-Young Kim Juan F. Pedraza Krylov complexity as an order parameter for quantum chaotic-integrable transitions Physical Review Research |
| title | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| title_full | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| title_fullStr | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| title_full_unstemmed | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| title_short | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| title_sort | krylov complexity as an order parameter for quantum chaotic integrable transitions |
| url | http://doi.org/10.1103/PhysRevResearch.7.023028 |
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