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Register a new userEnergy-resolved spatial inhomogeneity of disordered Mott systems
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We investigate the effects of weak to moderate disorder on the T=0 Mott metal-insulator transition in two dimensions. Our model calculations demonstrate that the electronic states close to the Fermi energy become more spatially homogeneous in the critical region. Remarkably, the higher energy states show the opposite behavior: they display enhanced spatial inhomogeneity precisely in the close vicinity to the Mott transition. We suggest that such energy-resolved disorder screening is a generic property of disordered Mott systems.
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We elucidate the mechanism by which a Mott insulator transforms into a non-Fermi liquid metal upon increasing disorder at half filling. By correlating maps of the local density of states, the local magnetization and the local bond conductivity, we find a collapse of the Mott gap toward a V-shape pseudogapped density of states that occurs concomitantly with the decrease of magnetism around the highly disordered sites but an increase of bond conductivity. These metallic regions percolate to form an emergent non-Fermi liquid phase with a conductivity that increases with temperature. Bond conductivity measured via local microwave impedance combined with charge and spin local spectroscopies are ideal tools to corroborate our predictions.
We calculate ground-state energies and density distributions of Hubbard superlattices characterized by periodic modulations of the on-site interaction and the on-site potential. Both density-matrix renormalization group and density-functional methods are employed and compared. We find that small variations in the on-site potential $v_i$ can simulate, cancel, or even overcompensate effects due to much larger variations in the on-site interaction $U_i$. Our findings highlight the importance of nanoscale spatial inhomogeneity in strongly correlated systems, and call for reexamination of model calculations assuming spatial homogeneity.
A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.
While the coherent potential approximation (CPA) is the prevalent method for the study of disordered electronic systems, it fails to capture non-local correlations and Anderson localization. To incorporate such effects, we extend the dual fermion approach to disordered non-interacting systems using the replica method. Results for single- and two- particle quantities show good agreement with cluster extensions of the CPA; moreover, weak localization is captured. As a natural extension of the CPA, our method presents an alternative to the existing cluster theories. It can be used in various applications, including the study of disordered interacting systems, or for the description of non-local effects in electronic structure calculations.
The Mott-Anderson transition in the disordered charge-transfer model displays several new features in comparison to what is found in the disordered single-band Hubbard model, as recently demonstrated by large-scale computational (statistical dynamical mean field theory) studies. Here we show that a much simpler typical medium theory approach (TMT-DMFT) to the same model is able to capture most qualitative and even quantitative aspects of the phase diagram, the emergence of an intermediate electronic Griffiths phase, and the critical behavior close to the metal-insulator transition. Conceptual and mathematical simplicity of the TMT-DMFT formulation thus makes it possible to gain useful new insight into the mechanism of the Mott-Anderson transition in these models.
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