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arXiv · 2407.00155

Krylov complexity for 1-matrix quantum mechanics

Niloofar Vardian
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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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Niloofar Vardian. 2024-06-28. Krylov complexity for 1-matrix quantum mechanics. https://arxiv.org/abs/2407.00155

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