  We discuss quantum phase transition by an exactly solvable model in the dual
gravity setup. By considering the effect of the scalar condensation on the
fermion spectrum near the quantum critical point(QCP), we find that there is a
topologically protected fermion zero mode associated with the metal to
insulator transition. We also show that the strange metal phase with T-linear
resistivity emerges at high enough temperature as far as the gravity has a
horizon. The phase boundaries are calculated according to the density of
states, giving insights on structures of the phase diagram near the QCP.
