Krylov complexity as an order parameter for quantum chaotic-integrable transitions
- URL: http://arxiv.org/abs/2407.17054v1
- Date: Wed, 24 Jul 2024 07:32:27 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 recently 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 before settling into a well-understood late-time plateau.
We demonstrate that the KCP effectively identifies chaotic-integrable transitions in the mass-deformed Sachdev-Ye-Kitaev model at both infinite and finite temperature.
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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 the mass-deformed Sachdev-Ye-Kitaev model at both infinite and finite temperature, aligning with results from spectral statistics and OTOCs. Our findings offer a new diagnostic tool for quantum chaos that is operator-independent, potentially leading to more `universal' insights and a deeper understanding of general properties in quantum chaotic systems.
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