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