Department of Physics • University of Cologne

We explore the intriguing spatial patterns that emerge in a two-dimensional spatially inhomogeneous Katz-Lebowitz-Spohn (KLS) driven lattice gas with attractive nearest-neighbor interactions. The domain is split into two regions with hopping rates governed by different temperatures T > T_c and T_c, respectively, where T_c indicates the critical temperature for phase ordering, and with the temperature boundaries oriented perpendicular to the drive. In the hotter region, the system behaves like the (totally) asymmetric exclusion processes (TASEP), and experiences particle blockage in front of the interface to the critical region. To explain this particle density accumulation near the interface, we have measured the steady-state current in the KLS model at T > T_c and found it to decay as 1/T. In analogy with TASEP systems containing "slow" bonds, transport in the high-temperature subsystem is impeded by the lower current in the cooler region, which tends to set the global stationary particle current value. This blockage is induced by the extended particle clusters, growing logarithmically with system size, in the critical region. We observe the density profiles in both high-and low- temperature subsystems to be similar to the well-characterized coexistence and maximal-current phases in (T)ASEP models with open boundary conditions, which are respectively governed by hyperbolic and trigonometric tangent functions. Yet if the lower temperature is set to T_c, we detect marked fluctuation corrections to the mean-field density profiles, e.g., the corresponding critical KLS power law density decay near the interfaces into the cooler region. If the temperature interface is aligned parallel to the drive, we observe the cooler region to act as an absorbing sink for particle transport, with blockages emerging at the subsystem boundaries.

Metal-insulator transitions (MIT), driven entirely by strong electron-electron interactions and/or disorder, continue to underpin many novel phenomena in quantum matter. We study disorder-driven MITs in the "strong disorder" category using a novel semi-analytic cluster adaptation of dynamical mean-field theory (CDMFT) for the simplest, binary-alloy disorder (also known as spinless Falicov-Kimball, or "simplified" Hubbard) model. Such an (oversimplified) model is a caricature for a disordered system where mobile electrons interact strongly with positionally random, localized charges. We uncover anomalous quantum criticality in the full dc conductivity tensor across the MIT which, remarkably, is reminiscent of "Mott quantum criticality" that obtains at the low-T end-point of the line of first-order transitions in the Hubbard model (experimentally best studied for 2D organics). Interestingly, such novel criticality is also found to underpin thermal transport (heat conductivity, Seebeck co-efficient, Lorenz number) across the MIT. Moreover, we also provide an explicit realization of the famed "universal dielectric response" (UDR) of Jonscher in optical responses across the MIT. The associated stretched-exponential relaxation in the long-time dielectric response strongly suggests anomalous diffusion, an emergent "electron glassy" dynamics and weak ergodicity breaking. These findings suggest that a truly novel type of carrier localization obtains in the "strong disorder" limit.