The emergence of strange metal and topological liquid near quantum critical point in a solvable model

We discuss quantum phase transition by a 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. Unlike the topological insulator, our zero mode is for the bulk of the material, not the edge. We also show that the strange metal phase with T-linear resistivity emerges at high enough temperature as far as a horizon exists. The phase boundaries calculated according to the density of states allow us understanding the structures of the phase diagram near the QCP.