  The periodic Anderson model is a classic theoretical model for understanding
novel physics in heavy fermion systems. Here, we modify it with the
Sachdev-Ye-Kitaev interaction, (random all-to-all interaction) thus the
resultant model admits an exact solution at large-$N$ (e.g. spin flavor) limit.
By analytical field theory arguments and numerical calculations, we establish
that the system supports a low-temperature (heavy) Fermi liquid and more
interesting a non-Fermi liquid solution at elevated temperature/energy. For
physical observable, the latter one contributes a sharp peak at Fermi energy
for spectral function, a non-Fermi liquid-like $T^{-1}$ resistivity and shows a
robust Fano lineshape in tunneling spectrum. This system may be simulated by
ultracold atom gases and can serve as a good playground for studying many
ubiquitous symmetry-breaking instabilities like unconventional
superconductivity or topological orders in generic heavy fermion systems.
