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In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner–Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition. We compare the available experimental data on these systems to three existing theoretical scenarios: spinon theory, Dynamical Mean Field Theory (DMFT) and percolation theory. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response. 

We study many‐body localization (MBL) from the perspective of integrals of motion (IOMs). MBL can be understood phenomenologically through the existence of macroscopically many localized IOMs. We develop a systematic procedure based on IOM to calculate many‐body quantities. Displacement transformations made clear that any operator can be expanded in 1‐,2‐ ...n‐particles terms. We use this property to develop a systematic procedure to approximately calculate IOMs and many‐body quantities. We characterize the decay with distance of the IOM's and their interactions through effective localization lengths. For all values of disorder the typical IOMs are localized, suggesting the importance of rare fluctuations in understanding the MBL‐to‐ergodic transition.image