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Recent studies of electrical transport, both theoretical and experimental,near the bandwidth-tuned Mott metal-insulator transition have uncoveredapparent quantum critical scaling of the electrical resistivity at elevatedtemperatures, despite the fact that the actual low-temperature phase transitionis of first order. This raises the question whether there is a hidden Mottquantum critical point. Here we argue that the dynamical mean-field theory ofthe Hubbard model admits, in the low-temperature limit, asymptoticallyscale-invariant (i.e. power-law) solutions, corresponding to the metastableinsulator at the boundary of metal-insulator coexistence region, which can belinked to the physics of the pseudogap Anderson model. While ourstate-of-the-art numerical renormalization group calculations reveal that thisasymptotic regime is restricted to very small energies and temperatures andhence difficult to access numerically, we uncover the existence of a widecrossover regime where the single-particle spectrum displays a \emph{different}power law. We show that it is this power-law regime, corresponding toapproximate local quantum criticality, which is continuously connected to andresponsible for the apparent quantum critical scaling above the classicalcritical end point. We connect our findings to experiments on tunable Mottmaterials.

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling