论文标题
在有限温度下的耦合SYK模型
The Coupled SYK model at Finite Temperature
论文作者
论文摘要
Sachdev-Ye-Kitaev（Syk）模型在0+1尺寸中描述了$ n $随机相互作用的Majorana fermions，被发现是一种可解决的紫外线完整玩具模型，用于几乎是ADS $ _2 $ _2 $ dilaton重力中的全息二元性。参考。 [1]通过耦合两个相同的SYK模型，提出了一个修改模型，该模型在低能限制下对全局ADS $ _2 $几何形状是双重的。该几何形状是“永恒的虫洞”，因为两个边界是因果关系的。升高温度驱动霍金页，例如从永恒的虫洞几何形状过渡到两个带有耦合物质场的脱节的黑洞。为了进一步了解耦合的SYK模型，在这项工作中，我们通过实时求解Schwinger-Dyson方程来研究该系统的有限温度光谱函数。我们在低温阶段发现该系统通过与重新归一化的单粒子间隙弱相互作用的费米片进行了很好的描述，而在高温阶段，系统的系统是强烈的相互作用，并且单粒子峰合并。我们还研究了频谱函数的$ q $依赖性。
Sachdev-Ye-Kitaev (SYK) model, which describes $N$ randomly interacting Majorana fermions in 0+1 dimension, is found to be an solvable UV-complete toy model for holographic duality in nearly AdS$_2$ dilaton gravity. Ref. [1] proposed a modified model by coupling two identical SYK models, which at low-energy limit is dual to a global AdS$_2$ geometry. This geometry is an "eternal wormhole" because the two boundaries are causally connected. Increasing the temperature drives a Hawking-Page like transition from the eternal wormhole geometry to two disconnected black holes with coupled matter field. To gain more understanding of the coupled SYK model, in this work, we study the finite temperature spectral function of this system by numerical solving the Schwinger-Dyson equation in real-time. We find in the low-temperature phase the system is well described by weakly interacting fermions with renormalized single-particle gap, while in the high temperature phase the system is strongly interacting and the single-particle peaks merge. We also study the $q$ dependence of the spectral function.
