From Dyson Models to Many-Body Quantum Chaos

• URL: http://arxiv.org/abs/2302.00917v1
• Date: Thu, 2 Feb 2023 07:33:10 GMT
• Title: From Dyson Models to Many-Body Quantum Chaos
• Abstract summary: We show that emphdelocalization is the dominant process in the single-particle to many-body chaotic transition. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the mechanisms underlying many-body quantum chaos is one of the big challenges in theoretical physics. We tackle this problem by considering a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows to disambiguate between operator growth and \emph{delocalization}, showing that the latter is the dominant process in the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians, in this case up to dimension $2^{19}\times 2^{19}$. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

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