  Exoplanetary observations reveal that the occurrence rate of hot Jupiters is
correlated with star clustering. In star clusters, interactions between
planetary systems and close fly-by stars can significantly change the
architecture of primordially coplanar, circular planetary systems. Flybys in
dense clusters have a significant impact on hot Jupiter formation via
activation of high eccentricity excitation mechanisms such as the
Zeipel-Lidov-Kozai (ZLK) effect and planet-planet scattering. Previous studies
have shown that if there are two giant planets in the planetary system, close
flybys can efficiently activate the ZLK mechanism, thus triggering high
eccentricity tidal migration and ultimately form hot Jupiters in star clusters.
Here we extend our previous study with a multi-planet (triple) system. We
perform high precision, high-accuracy few-body simulations of stellar flybys
and subsequent planetary migration within the perturbed planetary systems using
the code {\tt SpaceHub}. Our simulations demonstrate that a single close flyby
on a multi-planet system in a cluster can activate secular chaos and ultimately
lead to hot Jupiter formation via high eccentricity migration. We find that the
hot Jupiter formation rate per system increases with both the size of the
planetary system as well as with the mass of the outer planet, and we quantify
the relative formation fractions for a range of parameters. Hot Jupiters formed
via secular chaos are expected to be accompanied by massive companions with
very long periods. Our study further shows that this flyby-induced secular
chaos is preferred in low-density clusters where multi-planet systems are more
likely to survive, and that it contributes a significant fraction of the hot
Jupiter formation in star clusters compared to the flyby-induced ZLK mechanism.
