We numerically study a model of interacting spin-$1/2$ electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by $T$-linear Planckian behavior, $\omega /T$ scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The $\omega /T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a “skewed” non-Fermi liquid.

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• Quantum criticality
• Quantum phase transitions
• Cuprates
• Sachdev-Ye-Kitaev model