In contrast to the first-order correlation-driven Mott metal-insulator transition (MIT), continuous disorder-driven transitions are intrinsically quantum critical. Here, we investigate transport quantum criticality in the Falicov-Kimball model, a representative of the latter class in the "strong disorder" category. Employing cluster-dynamical mean-field theory (CDMFT), we find clear and anomalous quantum critical scaling behavior manifesting as perfect mirror symmetry of scaling curves on both sides of the MIT. Surprisingly, we find that the beta-function, β(g), scales like log(g) deep into the bad-metallic phase as well, providing sound unified basis for these findings. We argue that such "strong localization" quantum criticality may manifest in real three-dimensional systems where disorder effects are more important than electron-electron interactions.PACS numbers: 74.25.Jb, 71.27.+a, The weak localization (WL) of non-interacting electrons due to disorder is now well understood within the scaling formalism [1] as a genuine quantum phase transition. In spite of its extensive successes [2], further experimental developments [3,4] present compelling evidence for a different kind of quantum criticality that requires non-trivial extensions of the WL paradigm. It has long been suggested, both experimentally [5] and more recently, theoretically [6] that electron-electron interactions in a disordered system can cause a metal-insulator transition (MIT) in D = 2 dimensions. Another possibility is that the experiments may be probing the "strong localization" region of a disorder model, i.e, in a regime k F l ≤ 1, opposite to that where WL theory works. This is supported by the observation that features at odds with the WL predictions seem to be qualitatively similar for D = 2, 3 systems [4], as well as the fact that observed resistivities can greatly exceed (2 − 3) /e 2 (the Mott-IoffeRegel (MIR) limit), reaching unprecedentedly high values O(500 − 700) /e 2 . Further, beautiful "mirror" symmetry and associated scaling behaviors in transport, along with anomalous critical exponents suggestive of glassy freezing close to the MIT are known for the 2D electron gas in Si [3,4]. In these cases, either of the two scenarios above can cause the perturbative approach underlying WL to break down. This is because the infra-red pole structure of the one-fermion propagator is supplanted by a branchcut, putting the very notion of well-defined Landau-like quasiparticles in trouble in bad metals close to the MIT. Such anomalous features as the above are also to be found in systems close to purely correlation-driven Mott transitions [7]. For e.g, while resistivity curves (ρ dc (T, X), X a control parameter, e.g, external pressure) weakly depend upon X at high temperature T , they rapidly converge toward either metallic or insulating branches at low T . The "Mott" quantum critical aspect is rather clearly borne out by beautiful scaling behavior and "mirror" symmetry of the scaling (beta) functions. Since dynamical mean-field theory (DMFT)...

We study the thermalization, after sudden and slow quenches, of an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to non-interacting lead fermions and can be realized in a graphene flake connected to external leads. A sudden quench to the NFL leads to rapid thermalization via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL shows multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time τ , we find that the excitation energy generated has a remarkable intermediate-τ non-analytic power-law dependence, τ −η with η < 1, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. Our study gives an explicit demonstration of the intriguing contrasts between the out-of-equilibrium dynamics of a NFL and a FL in terms of their thermalization and approach to adiabaticity.One of the major frontiers in condensed matter physics is to describe gapless phases of interacting fermions without any quasiparticles, namely non Fermi liquids (NFL) [1]. Recently, new insights about fundamental differences between NFLs and Fermi liquids (FL) have been gained in terms of many-body quantum chaos and thermalization. This new impetus has come from exciting developments in a class of NFLs described by Sachdev-Ye-Kitaev (SYK) model, [2][3][4] and its extensions [5][6][7][8][9][10][11][12][13], and their connections with black holes in quantum gravity [3,14,15]. In particular, the model proposed in ref. [6] classifies the SYK NFL and a FL as two distinct chaotic fixed points, separated by a quantum phase transition (QPT). In this characterization, the NFL thermalizes much faster than the FL, as quantified by a rate of the onset of chaos or the Lyapunov exponent [3,6,16].However, the Lyapunov exponent is computed from an equilibrium dynamical correlation, the so-called outof-time-ordered correlator [3,4,17]. Here, using the model of ref.[6] as a template, we ask whether such contrast between the NFL and FL persists even for thermalization from a completely out-of-equilibrium situation, e.g. a quantum quench. Remarkably, the exactly solvable nature of the model allows us to study its full nonequilibrium evolution exactly. By using non-equilibrium Keldysh field theory in the thermodynamic limit, as well as numerical exact diagonalization (ED) for finite systems, we demonstrate a drastic difference in thermalization rates for the NFL and FL after a sudden quench. Furthermore, the Landau description of a FL is based on the concept of adiabatic time evolution from a noninteracting system under slow switching on of the interaction, without encountering a phase transition. Is it possible to evolve an NFL adiabatically to the FL and vice versa? We argue that such evolution is not possible here due to another intriguing aspect of the SYK NFL, namely the finite zero-temperature residual e...