Anomalous Local Criticality in Heavy Fermion Metals from Holography

We propose a holographic theory to explain numbers of anomalous critical phenomena observed in certain heavy-fermion metals, e.g. $\mathrm{CeCu_{5.9}Au_{0.1}}$ and $\mathrm{YbRh_{2}(Si_{0.95}Ge_{0.05}})_{2}$, which are incompatible with any conventional spin-density-wave quantum critical point theory. We show that the non-Gaussian nature of the fixed point from holography plays an essential role in the physics of these materials near a quantum critical point, which is not in the same universality class of the spin-density-wave type fixed point. The critical spin fluctuations at the non-Gaussian fixed point are strongly anisotropic, localized in spatial directions and critical in temporal direction with critical exponent 2/3 in frequency over temperature dependence at low temperature. The local critical exponent tends to unity which leads to a constant spin relaxation rate in the quantum critical regime at high temperature. The stability of the fixed point is also discussed.