Kondo screening and random-singlet formation in highly disordered systems

We propose a minimal model to capture the anomalous low-temperature thermodynamics of doped semiconductors, such as Si:P, across the metal-insulator transition. We consider pairs of local magnetic moments coupled to a highly disordered, non-interacting electronic bath that undergoes a metal-insulator transition with increasing doping. Using a large-$\mathcal{N}$ variational approach, we capture both the inhomogeneous local Fermi-liquid and the insulating random-singlet phase, and find that the local moment susceptibility exhibits a robust power-law behavior, $\chi(T) \propto T^{-\alpha}$, with $\alpha$ evolving smoothly with doping before saturating in the metal. Our results highlight the competition between Kondo screening and random-singlet formation as the key ingredient in constructing a complete theory for the low-temperature behavior of strongly disordered interacting systems.