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We propose that competition between Kondo and magnetic correlations resultsin a novel universality class for heavy fermion quantum criticality in thepresence of strong randomness. Starting from an Anderson lattice model withdisorder, we derive an effective local field theory in the dynamical mean-fieldtheory (DMFT) approximation, where randomness is introduced into bothhybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performingthe saddle-point analysis in the U(1) slave-boson representation, we reveal itsphase diagram which shows a quantum phase transition from a spin liquid stateto a local Fermi liquid phase. In contrast with the clean limit of the Andersonlattice model, the effective hybridization given by holon condensation turnsout to vanish, resulting from the zero mean value of the hybridization couplingconstant. However, we show that the holon density becomes finite when varianceof hybridization is sufficiently larger than that of the RKKY coupling, givingrise to the Kondo effect. On the other hand, when the variance of hybridizationbecomes smaller than that of the RKKY coupling, the Kondo effect disappears,resulting in a fully symmetric paramagnetic state, adiabatically connected withthe spin liquid state of the disordered Heisenberg model.

Competition between Kondo and RKKY correlations in the presence of strong randomness