论文标题
具有额外对角线扰动的SYK模型：特征值光谱中的相变
SYK model with an extra diagonal perturbation: phase transition in the eigenvalue spectrum
论文作者
论文摘要
我们研究了具有额外恒定源的SYK模型，即恒定矩阵或等效的对角矩阵，只有一个非零条目$λ_1$。通过使用分析组合学的方法，我们找到了该模型矩的精确表达式。我们进一步证明，当$λ_1>λ>λ^c_1 $时，该模型的频谱可能会有差距，从而在$λ_1$中表现出相变。在这种情况下，单个孤立的特征值从Syk的特征值分布中分离出来。我们通过分析超临界功能组成方案的奇异行为找到了这个单一特征值。在某些限制中，我们的结果恢复了具有非零均值条目的随机矩阵的结果。
We study the SYK model with an extra constant source, i.e. a constant matrix or equivalently a diagonal matrix with only one non-zero entry $λ_1$. By using methods from analytic combinatorics, we find exact expressions for the moments of this model. We further prove that the spectrum of this model can have a gap when $λ_1>λ^c_1$, thus exhibiting a phase transition in $λ_1$. In this case, a single isolated eigenvalue splits off from SYK's eigenvalues distribution. We located this single eigenvalue by analyzing the singular behavior of a supercritical functional composition scheme. In certain limit our results recover the ones of random matrices with non-zero mean entries.
