We perform a systematic study of incoherent transport in the high temperature crossover region of the half-filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form ρ(T, δU ) = ρc(T )f (T /To(δU )), with To(δU ) ∼ |δU | zν , and ρc(T ) ∼ T . The corresponding β-function displays a "strong coupling" form β ∼ ln(ρc/ρ), reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.

The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of quantum Widom lines and present a detailed discussion that highlights its physical meaning when used in the context of quantum phase transitions.

Bad-Metal (BM) behavior featuring linear temperature dependence of the resistivity extending to well above the Mott-Ioffe-Regel (MIR) limit is often viewed as one of the key unresolved signatures of strong correlation. Here we associate the BM behavior with the Mott quantum criticality by examining a fully frustrated Hubbard model where all long-range magnetic orders are suppressed, and the Mott problem can be rigorously solved through Dynamical Mean-Field Theory. We show that for the doped Mott insulator regime, the coexistence dome and the associated first-order Mott metal-insulator transition are confined to extremely low temperatures, while clear signatures of Mott quantum criticality emerge across much of the phase diagram. Remarkable scaling behavior is identified for the entire family of resistivity curves, with a quantum critical region covering the entire BM regime, providing not only insight, but also quantitative understanding around the MIR limit, in agreement with the available experiments.PACS numbers: 71.27.+a,71.30.+h Metallic transport inconsistent with Fermi liquid theory has been observed in many different systems; it is often linked to quantum criticality around some ordering phase transition [1, 2]. Such behavior is notable near quantum critical points in good conductors, for example in heavy fermion compounds [3, 4]. In several other classes of materials, however, much more dramatic departures form conventional metallic behavior are clearly observed, where resistivity still rises linearly with temperature, but it reaches paradoxically large values, well past the MIR limit [5, 6]. This "Bad-Metal" (BM) behavior [7], was first identified in the heyday of high-temperature superconductivity, in materials such as La 2−x Sr x CuO 4 [8]. While the specific copper-oxide family and related high-T c materials remain ill-understood and marred with controversy, it soon became clear that BM behavior is a much more general feature [6] of materials close to the Mott metal-insulator transition (MIT) [9]. Indeed, it has been clearly identified also in various oxides [10, 11], organic Mott systems [12][13][14], as well as more recently discovered families of iron pnictides [15]. Despite years of speculation and debate, so far its clear physical interpretation has not been established.To gain reliable insight into the origin of BM behavior, it is useful to examine an exactly solvable model system, where one can suppress all possible effect associated with the approach to some broken symmetry phase, or those specific to low dimensions and a given lattice structure. This can be achieved by focusing on the "maximally frustrated Hubbard model", where an exact solution can be obtained by solving Dynamical Mean-Field Theory (DMFT) equations [16] in the paramagnetic phase. Although various aspects of the DMFT equation have been studied for more than twenty years, only very recent work [17,18] established how to identify the quantum critical (QC) behavior associated with the interaction-driven Mott transition at ...