近日，中国人民大学张芃团队研究了混合布朗SYK-哈伯德模型：从谱函数到量子混沌。相关论文于2025年11月24日发表在《高能物理杂志》上。

理解强关联系统中复杂关联的涌现仍是量子多体物理中的基本挑战。一个有效的方法是开发可解析的简化模型，以捕捉真实系统所共有的普适特性。

研究组引入了布朗SYK-哈伯德模型，该模型将Sachdev-Ye-Kitaev（SYK）模型的全连接随机相互作用与局域哈伯德型相互作用相结合。这种混合构造使得研究非局域随机动力学与局域关联效应的相互作用成为可能：(1) 随着相互作用强度增加，单粒子谱从单一峰结构转变为双峰结构，标志着Mott特性（Mottness）的出现；(2) 在强哈伯德相互作用下，谱形因子在长时间极限达到平台值前，会随演化时间经历一系列动态跃迁；(3) 通过求和一系列修正的阶梯图计算出自旋-时间无序关联函数（OTOC），确定了量子李雅普诺夫指数，并揭示了其对分支时间限制的违反。该工作建立了一个新的可解析研究平台，用于探索哈伯德相互作用在混沌多体系统中的影响。

附：英文原文

Title: Hybrid Brownian SYK-Hubbard model: from spectral function to quantum chaos

Author: Sun, Ning, Zhang, Peng, Zhang, Pengfei

Issue&Volume: 2025-11-24

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.

DOI: 10.1007/JHEP11(2025)150

Source: https://link.springer.com/article/10.1007/JHEP11(2025)150