A holographic description on the antiferromagnetic quantum phase transition (QPT) induced by the magnetic field and the criticality in the vicinity of the quantum critical point 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 ${\mathrm{AdS}}_2$ in the IR region, which confirms that the dual boundary theory is a strong coupling theory with dynamic exponent $z=2$ and logarithmic corrections appearing. We also compare them with the results from the Hertz model by solving the RG equation at its upper critical dimension and with some experimental data from pyrochlores ${\mathrm{Er}}_{2-2x}{\mathrm{Y}}_{2x}{\mathrm{Ti}}_2{\mathrm{O}}_7$ and ${\mathrm{BiCoPO}}_5$.

• Received 6 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.046005