论文标题
SYK $ _ {2} $模型中的相关障碍
Correlated Disorder in the SYK$_{2}$ model
论文作者
论文摘要
我们通过详细的光谱分析和将模型与2-和4点源一起使用，研究了$ n $ majorana fermions的SYK $ _ {2} $模型，并通过随机的二次相互作用进行随机相互作用。特别是，我们通过从分区函数推广到生成函数来定义广义频谱形式和水平间距分布函数。对于$ n = 2 $，我们获得了广义频谱颜料的精确解决方案。它表现出与带有源术语的较高$ n $案例的质量相似行为。确切的解决方案有助于了解广义光谱构成的行为。我们计算广义级别间距分布函数和生成函数定义的相邻间隙比的平均值。对于具有4分源术语的SYK $ _2 $模型，我们在理论的近乎整合区域中找到了高斯单位合奏行为，这表明过渡到混乱。通过展开的光谱，通过广义光谱形式的连接部分证实了这种行为。偏离这种高斯随机矩阵行为，因为源项的相对强度增加与观察到的观察是，仅在没有SYK $ _2 $耦合的情况下，仅四点源项就打开了，它表现出来自光谱形式的集成频谱，并且在大$ n $ limit中的级别型号和级别的间隔函数。
We study the SYK$_{2}$ model of $N$ Majorana fermions with random quadratic interactions through a detailed spectral analysis and by coupling the model to 2- and 4-point sources. In particular, we define the generalized spectral form factor and level spacing distribution function by generalizing from the partition function to the generating function. For $N=2$, we obtain an exact solution of the generalized spectral form factor. It exhibits qualitatively similar behavior to the higher $N$ case with a source term. The exact solution helps understand the behavior of the generalized spectral form factor. We calculate the generalized level spacing distribution function and the mean value of the adjacent gap ratio defined by the generating function. For the SYK$_2$ model with a 4-point source term, we find a Gaussian unitary ensemble behavior in the near-integrable region of the theory, which indicates a transition to chaos. This behavior is confirmed by the connected part of the generalized spectral form factor with an unfolded spectrum. The departure from this Gaussian random matrix behavior as the relative strength of the source term is increased is consistent with the observation that the 4-point source term alone, without the SYK$_2$ couplings turned on, exhibits an integrable spectrum from the spectral form factor and level spacing distribution function in the large $N$ limit.
