Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos

• URL: http://arxiv.org/abs/2510.16401v1
• Date: Sat, 18 Oct 2025 08:29:15 GMT
• Title: Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Authors: Ning Sun, Peng Zhang, Pengfei Zhang,
• Abstract summary: We introduce the Brownian SYK-Hubbard model, which combines the all-to-all random interactions of the Sachdev-Ye-Kitaev (SYK) model with on-site Hubbard-type interactions.<n>Our results establish a new analytically tractable platform for exploring the effects of Hubbard interactions in chaotic many-body systems.
• Score: 12.63172482253749
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the emergence of complex correlations in strongly interacting systems remains a fundamental challenge in quantum many-body physics. One fruitful approach is to develop solvable toy models that encapsulate universal properties shared by realistic systems. In this work, we introduce the Brownian SYK-Hubbard model, which combines the all-to-all random interactions of the Sachdev-Ye-Kitaev (SYK) model with on-site Hubbard-type interactions. This hybrid construction enables the study of the interplay between nonlocal random dynamics and local correlation effects: (1) As the interaction strength increases, the single-particle spectrum exhibits a transition from a single peak to a two-peak structure, signaling the onset of Mottness. (2) The spectral form factor undergoes a sequence of dynamical transitions as the evolution time increases before reaching the plateau in the long-time limit under strong Hubbard interactions. (3) The out-of-time-order correlator is computed by summing a series of modified ladder diagrams, which determines the quantum Lyapunov exponent and reveals a violation of the bound on branching time. Our results establish a new analytically tractable platform for exploring the effects of Hubbard interactions in chaotic many-body systems.

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