Mean field theory and holographic Kondo lattice

We study a non-relativistic field theory model for the Kondo lattice. The Fierz identity and the mean-field approximation transform our model into an Anderson-like model that is stabilized by a scalar-type s-d interaction term. Numerical minimization of the thermodynamic potential shows that the Kondo condensation forms when the temperature is low, and the s-d coupling is strong. The formation of the Kondo condensation at zero temperature turns out to give a first-order quantum phase transition. Though these results are very suggestive and consistent with previous large-N studies, they work only when the mean-field theory is justified in strong coupling, as usual. We build a holographic model as an effective mean-field theory for the Kondo lattice with strong coupling, by considering interacting two-flavor spinors, one in standard quantization and the other one in the mixed quantization, both them coupled with scalar orders representing the Kondo condensation. Our model realizes the extended Fermi surface as well as the large fermion mass of heavy fermion physics in the strong coupling regime.