Krylov complexity as an order parameter for quantum chaotic-integrable transitions
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| Format: | Preprint |
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2024
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| author | Baggioli, Matteo Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Pedraza, Juan F. |
| author_facet | Baggioli, Matteo Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Pedraza, Juan F. |
| contents | Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are 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 | Preprint |
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arxiv_https___arxiv_org_abs_2407_17054 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Krylov complexity as an order parameter for quantum chaotic-integrable transitions Baggioli, Matteo Huh, Kyoung-Bum Jeong, Hyun-Sik Kim, Keun-Young Pedraza, Juan F. High Energy Physics - Theory Chaotic Dynamics Quantum Physics Krylov complexity has recently emerged as a new paradigm to characterize quantum chaos in many-body systems. However, which features of Krylov complexity are 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. |
| title | Krylov complexity as an order parameter for quantum chaotic-integrable transitions |
| topic | High Energy Physics - Theory Chaotic Dynamics Quantum Physics |
| url | https://arxiv.org/abs/2407.17054 |