  We show that the quantum critical point (QCP) between a diffusive metal and
ferromagnetic (or antiferromagnetic) phases in the SYK chain has a
gravitational description corresponding to the double-trace deformation in an
AdS$_2$ chain. Specifically, by studying a double-trace deformation of a $Z_2$
scalar in an AdS$_2$ chain where the $Z_2$ scalar is dual to the order
parameter in the SYK chain, we find that the susceptibility and renormalization
group equation describing the QCP in the SYK chain can be exactly reproduced in
the holographic model. Our results suggest that the infrared geometry in the
gravity theory dual to the diffusive metal of the SYK chain is also an AdS$_2$
chain. We further show that the transition in SYK model captures universal
information about double-trace deformation in generic black holes with near
horizon AdS$_2$ spacetime.
