Yukawa-Sachdev-Ye-Kitaev模型中随机矩阵统计的出现：谱关联与Krylov复杂度
Onset of random-matrix statistics in the Yukawa-Sachdev-Ye-Kitaev model: Spectral correlations and Krylov complexity
- Fudan University（复旦大学）
- Asia Pacific Center for Theoretical Physics（亚太理论物理中心）
- Pohang University of Science and Technology（韩国科学技术院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究通过精确对角化分析YSYK模型，发现谱统计和Krylov复杂度在R≈0.3处出现随机矩阵统计，且峰值高度可识别对称性类别，为腔QED实现混沌提供了依据。
AI中文摘要：
Yukawa-Sachdev-Ye-Kitaev (YSYK)模型是一种可解的非费米液体模型，并提出了腔量子电动力学（cavity-QED）实现方案。该模型通过强度为g的随机Yukawa耦合，将N个复费米子与M个频率为ω0的玻色子耦合在一起，其动力学仅依赖于R≡ω0/g^(2/3)。当R≪1时，玻色子运动缓慢，表现为静态随机背景，费米子在其中自由运动；而当R≫1时，玻色子仅被虚激发，产生秩为M的随机四费米子相互作用，对于M≥2，该相互作用通常是混沌的。利用无限温度下的精确对角化，我们通过展开谱统计和热场双态的Krylov复杂度，追踪了这些极限之间随机矩阵统计的出现。对于复耦合，能级间距分布从泊松分布演化为高斯幺正系综（GUE）统计，谱形状因子出现关联洞和斜坡，且在展开谱上计算的Krylov复杂度在其晚期平台之上出现峰值，其高度达到GUE值。所有诊断都将起始点定位在R≈0.3附近，增加玻色子模式会将其移至更小的R。这描绘了腔QED实现将展现随机矩阵谱关联的参数区域。另一方面，实耦合给出向高斯正交系综（GOE）统计的相同交叉，并且在两者之间的插值过程中，峰值高度遵循平均间隙比，因此峰值既能识别混沌的起始，也能识别对称性类别。在不展开谱的情况下，两类中的峰值高度均比其随机矩阵值低约20%，我们将此归因于非半圆态密度，并且在更大的R下，玻色子数带会减缓态在Krylov空间中的扩散。
英文摘要：
The Yukawa-Sachdev-Ye-Kitaev (YSYK) model, a solvable model of non-Fermi liquids with a proposed cavity-QED realization, couples $N$ complex fermions to $M$ bosons of frequency $ω_0$ through random Yukawa couplings of strength $g$, and its dynamics depends only on $R\equivω_0/g^{2/3}$. For $R\ll1$ the bosons are slow and act as a static random background in which the fermions are free, while for $R\gg1$ they are only virtually excited and generate a random four-fermion interaction of rank $M$, which is generically chaotic for $M\geq2$. Using exact diagonalization at infinite temperature, we follow the emergence of random-matrix statistics between these limits with unfolded spectral statistics and the Krylov complexity of the thermofield-double state. For complex couplings the level-spacing distribution evolves from Poisson to Gaussian-unitary-ensemble (GUE) statistics, the spectral form factor develops a correlation hole and a ramp, and the Krylov complexity evaluated on the unfolded spectrum develops a peak above its late-time plateau whose height reaches the GUE value. All diagnostics locate the onset around $R\approx0.3$, and adding boson modes moves it to smaller $R$. This delineates the parameter regime in which a cavity-QED realization would display random-matrix spectral correlations. On the other hand, real couplings give the same crossover towards Gaussian-orthogonal-ensemble (GOE) statistics, and along an interpolation between the two the peak height follows the mean gap ratio, so the peak identifies the symmetry class as well as the onset of chaos. Without unfolding the peak stays about 20$\%$ below its random-matrix value in both classes, which we trace to the non-semicircular density of states, and at larger $R$ the boson-number bands slow down the spreading of the state in Krylov space.
