Holographic antiferromganetic quantum criticality and AdS$_2$ scaling limit

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$_5$.