Krylov complexity as an order parameter for quantum chaotic-integrable transitions

• URL: http://arxiv.org/abs/2407.17054v3
• Date: Thu, 7 Nov 2024 09:22:34 GMT
• Title: Krylov complexity as an order parameter for quantum chaotic-integrable transitions
• Authors: Matteo Baggioli, Kyoung-Bum Huh, Hyun-Sik Jeong, Keun-Young Kim, Juan F. Pedraza,
• Abstract summary: Krylov complexity has emerged as a new paradigm to characterize quantum chaos in many-body systems. Recent insights have revealed that in quantum chaotic systems Krylov state complexity exhibits a distinct peak during time evolution. 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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