  A holographic description on antiferromagnetic quantum phase transition (QPT)
induced by magnetic field and the criticality in the vicinity of quantum
critical point (QCP) have been investigated numerically recently. In this
paper, we show that the properties of QPT in this holographic model are
governed by a CFT dual to the emergent AdS$_2$ in the IR region, which confirms
that the dual boundary theory is a strong coupling theory with dynamic exponent
$z=2$ and logarithmic corrections appear. We also compare them with the results
from Hertz model by solving RG equation at its upper critical dimension and
with some experimental data from pyrochlores Er$_{2-2x}$Y$_{2x}$Ti$_2$O$_7$ and
BiCoPO$_5$.
