  We present a JT gravity set up that reveals the evidence of (Euclidean)
wormhole to black hole phase transition at finite charge density and/or
chemical potential. We identify the low temperature phase of the system as the
charged wormhole solution. As the temperature of the system is increased, it
undergoes a first order phase transition to a two black hole system at finite
charge density. At the critical point ($T = T_0$) of the phase transition, both
the Free energy (density) and the charge undergoes a discontinuous change.
Finally, we conjectured that the field theory dual to this gravitational set up
is a two-site (uncoupled) complex SYK model at a finite chemical potential.
