  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.
