发表机构
Université de Montréal; Università di Roma Tor Vergata（蒙特利尔大学; 罗马托尔维加塔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对SYK哈密顿量，建立介观弱局域律与本征向量离域化估计，推导相关谱估计并得到体本征向量的高概率离域化界。
AI 中文摘要
我们针对SYK哈密顿量建立了介观弱局域律与定量本征向量离域化估计。对于满足q远小于N的1/2次方的偶数q，我们证明归一化Stieltjes变换在有界能量区间上一致收敛于标准高斯律的Stieltjes变换，收敛尺度低至qN的-1/2次方量级，误差包含对数因子。该结果在整个希尔伯特空间及每个费米子宇称扇区均成立。我们推导了介观本征值计数与谱形式因子估计，以及平均逆参与率界。对于固定q，我们还在任意确定正交基下得到了单个体本征向量的高概率ℓ^∞-离域化界。
英文摘要
We establish a mesoscopic local law and quantitative eigenvector-delocalization estimates for the Sachdev--Ye--Kitaev model (SYK) Hamiltonian of $N$ interacting Majorana fermions subject to a $q$-body interaction. For even $q\ll N^{\frac{1}{2}}$, we prove that the normalized Stieltjes transform is approximated, uniformly on bounded energy intervals, by an explicit deterministic profile which we construct as an asymptotic expansion in the proportion $α_{N,q}$ of anticommuting $q$-body interaction terms. The result holds both on the full Hilbert space and in each fermion-parity sector. We derive mesoscopic eigenvalue counting and spectral form factor estimates. For fixed $q$, we further obtain high-probability $\ell^\infty$-delocalization bounds in any deterministic orthonormal basis for individual bulk eigenvectors. These are the first mesoscopic laws and eigenvector delocalization estimates for the SYK Hamiltonian, which we obtain using the resolvent method.
Comments31 pages. Improved local law, added references
