Krylov complexity for 1-matrix quantum mechanics

• URL: http://arxiv.org/abs/2407.00155v3
• Date: Sat, 05 Oct 2024 07:27:05 GMT
• Title: Krylov complexity for 1-matrix quantum mechanics
• Authors: Niloofar Vardian,
• Abstract summary: This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM) We analyze the Lanczos coefficients derived from the correlation function, revealing their linear growth even in this integrable system. Our findings in both ground and thermal states of 1-MQM provide new insights into the nature of complexity in quantum mechanical models.
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• Abstract: This paper investigates the notion of Krylov complexity, a measure of operator growth, within the framework of 1-matrix quantum mechanics (1-MQM). Krylov complexity quantifies how an operator evolves over time by expanding it in a series of nested commutators with the Hamiltonian. We analyze the Lanczos coefficients derived from the correlation function, revealing their linear growth even in this integrable system. This growth suggests a link to chaotic behavior, typically unexpected in integrable systems. Our findings in both ground and thermal states of 1-MQM provide new insights into the nature of complexity in quantum mechanical models and lay the groundwork for further studies in more complex holographic theories.

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