We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g^{*} signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects.
We perform variational studies of the interaction-localization problem to describe the interaction-induced renormalizations of the effective (screened) random potential seen by quasiparticles. Here we present results of careful finite-size scaling studies for the conductance of disordered Hubbard chains at half-filling and zero temperature. While our results indicate that quasiparticle wave functions remain exponentially localized even in the presence of moderate to strong repulsive interactions, we show that interactions produce a strong decrease of the characteristic conductance scale g^{*} signaling the crossover to strong localization. This effect, which cannot be captured by a simple renormalization of the disorder strength, instead reflects a peculiar non-Gaussian form of the spatial correlations of the screened disordered potential, a hitherto neglected mechanism to dramatically reduce the impact of Anderson localization (interference) effects.
We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that describes short-range correlations near the Mott transition. We apply an Aharonov-Bohm magnetic flux, which generates a persistent current that can be related to the Thouless conductance. The magnitude of the current depends on both the strength of the screened disorder potential and the strength of electron-electron correlations, and the Anderson localization length can be extracted from the scaling of the current with system size. At half-filling, the persistent current is reduced by strong correlations when the interaction strength is large. Surprisingly, we find that the disorder potential is strongly screened in the large interaction limit, so that the localization length grows with increasing interaction strength even as the magnitude of the current is suppressed. This supports earlier dynamical mean-field-theory predictions that the elastic scattering rate is suppressed near the Mott transition.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
We study the one-dimensional Anderson-Hubbard model using the density-matrix renormalization-group method. The influence of disorder on the Tomonaga- Luttinger liquid behavior is quantitatively discussed. Based on the finite-size scaling analysis of density-density correlation functions, we find the following results: (i) the charge exponent is significantly reduced by disorder at low filling and near half filling, (ii) the localization length decays as $\ensuremath{\xi}\ensuremath{\sim}{\ensuremath{\Delta}}^{\ensuremath{-}2}$, where $\ensuremath{\Delta}$ is the disorder strength, independently of the on-site Coulomb interaction as well as band filling, and (iii) the localization length is strongly suppressed by the on-site Coulomb interaction near half filling in association with the formation of the Mott plateaus.
We present a large N solution of a microscopic model describing the Mott-Anderson transition on a finite-coordination Bethe lattice. Our results demonstrate that strong spatial fluctuations, due to Anderson localization effects, dramatically modify the quantum critical behavior near disordered Mott transitions. The leading critical behavior of quasiparticle wave functions is shown to assume a universal form in the full range from weak to strong disorder, in contrast to disorder-driven non-Fermi liquid ("electronic Griffiths phase") behavior, which is found only in the strongly correlated regime.
We consider the change in electron localization due to the presence of electron-electron repulsion in the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. We find rich nonmonotonic behavior of the localization length $\ensuremath{\xi}$ in two-dimensional systems, including an interaction-induced exponential enhancement of $\ensuremath{\xi}$ for small and intermediate disorders although $\ensuremath{\xi}$ remains finite. In three dimensions we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbard-gapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase.
In this thesis we consider a variational wave function approach as a possible route to describe the competition between disorder and strong electron-electron interaction in two dimensions. In particular we aim to obtain a transparent and physically intuitive understanding of the competition between these two localizing forces within the simplest model where they both are active, namely the disordered Hubbard model at half filling and in a square lattice. Our approach is based on an approximate form of the ground-state wave function, which we believe contains the physically relevant ingredients for a correct description of both the Mott and the Anderson insulators, where electrons are localized by the Coulomb repulsion and by disorder, respectively. For strongly interacting fermionic systems, a standard variational wave function is constructed by a correlation term acting on a Slater determinant, the latter being an uncorrelated metallic state. Previous variational calculations showed that a long-range density-density correlation factor, so called Jastrow factor, is needed to correctly describe the Mott insulator [9]. This term, which is collective by definition, correlates spatially charge uctuations, thus preventing their free motion that would otherwise imply metallic conductance. For this reason, our variational wave function does include such a term. Anderson localization is instead mostly a matter of single-particle wave functions, hence it pertains to the uncorrelated Slater determinant which the Jastrow factor acts onto. We consider both the case in which we enforce paramagnetism in the wave function and the case in which we allow for magnetic ordering. Summarizing briefly our results, we find that, when the variational wave function is forced to be paramagnetic, the Anderson insulator to Mott insulator transition is continuous. This transition can be captured by studying several quantities. In particular, a novel one that we have identified and that is easily accessible variationally is the disconnected density-density fluctuation at long wavelength, defined by lim where ^nq is the Fourier transform of the charge density at momentum q, (...) denotes quantum average at fixed disorder and the overbar represents the average over disorder configurations. We find that Ndisc q!0 is everywhere finite in the Anderson insulator and vanishes critically at the Mott transition, staying zero in the Mott insulator. When magnetism is allowed and the hopping only connects nearest neighbor sites, upon increasing interaction the paramagnetic Anderson insulator first turns antiferromagnetic and finally the magnetic and compressible Anderson insulator gives way to an incompressible antiferromagnetic Mott insulator. The optimized uncorrelated Slater determinant is always found to be the eigenstate of a disordered non-interacting effective Hamiltonian, which suggests that the model is never metallic. Finally, when magnetism is frustrated by a next to nearest neighbor hopping, the overall sequence of phases does not change. However, the paramagnetic to magnetic transition within the Anderson insulator basin of stability turns first order. Indeed, within the magnetically ordered phase, we find many almost degenerate paramagnetic states with well defined local moments. This is suggestive of an emerging glassy behavior when the competition between disorder and strong correlation is maximum.