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

Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e. power-law) solutions, corresponding to the metastable insulator at the boundary of metal-insulator coexistence region, which can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a \emph{different} power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.