The coupled SYK model at finite temperature
The coupled SYK model at finite temperature
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DOI：
10.1007/jhep05(2020)129
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发表时间：
2020-03
影响因子：
5.4
通讯作者：
X. Qi;Pengfei Zhang
中科院分区：
文献类型：
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作者：
X. Qi;Pengfei Zhang
描述N个0+ 1维随机相互作用的Majorana费米子的Sachdev-Ye-Kitaev（SYK）模型是一个可解的UV完全玩具模型.参考文献[1]提出了一个通过耦合两个完全相同的SYK模型的修正模型，该模型在低能极限下与全局AdS 2几何对偶。这个几何是一个“永恒的虫洞”，因为这两个边界是因果相连的。温度的增加驱动一个霍金-佩奇式的过渡，从永恒的虫洞几何形状到两个不连通的黑洞与耦合的物质场。为了更好地理解耦合SYK模型，本文通过实时数值求解Schwinger-Dyson方程，研究了该系统的有限温度谱函数。我们发现，在低温阶段的系统是很好地描述了弱相互作用的费米子与重整化单粒子间隙，而在高温阶段的系统是强相互作用和单粒子峰合并。我们还研究了谱函数的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.