Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.
Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.
The competition between the Mott transition and the Anderson localization in one-dimensional electron systems is studied with the bosonization and renormalization-group methods. The $\ensuremath{\beta}$ function is calculated up to second order in the strength of diagonal disorder by using a replica trick. It is found that sufficiently strong forward scattering by random impurities destroys the Mott-Hubbard gap, and backward scattering gives rise to Anderson localization for the resulting gapless state. On the other hand, if the umklapp interaction is strong enough, the Mott insulating state still overwhelms the Anderson localization.
We study the ground-state phase diagram of the Anderson-Hubbard model with correlated hopping at half-filling in one dimension. The Hamiltonian has a local Coulomb repulsion U and a disorder potential with local energies randomly distributed in the interval $(\ensuremath{-}W,+W)$ with equal probability, acting on the singly occupied sites. The hopping process which modifies the number of doubly occupied sites is forbidden. The hopping between nearest-neighbor singly occupied and empty sites or between singly occupied and doubly occupied sites has the same amplitude t. We identify three different phases as functions of the disorder amplitude W and Coulomb interaction strength U>0. When U<4t the system shows a metallic phase: (i) only when no disorder is present W=0 or an Anderson-localized phase, (ii) when disorder is introduced $W\ensuremath{\ne}0$. When U>4t the Anderson-localized phase survives as long as disorder effects dominate on the interaction effects, otherwise a Mott-insulator phase (iii) arises. Phases (i) and (ii) are characterized by a finite density of doublons and a vanishing charge gap among the ground state and the excited states. Phase (iii) is characterized by the vanishing density of doublons and a finite gap for the charge excitations.
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.
The interplay between Anderson localization and Mott localization is considered in the vicinity of one dimension for a collection of interacting spinless fermions or repulsive bosons. We demonstrate that in the absence of commensurability effects an Anderson localization transition does take place for d\ensuremath{\le}1. It is characterized by a critical dynamical exponent z having value z=2-d for d\ensuremath{\rightarrow}1-0, in disagreement with the previous claims that z always equals d. We find that there is only a localized phase for d>1 and expect that this similarity between free fermions and interacting quantum particles will be valid up to two dimensions. We also consider the competition between the effects of commensurability, disorder, and interaction in exactly one dimension. The outcome strongly depends on the order of umklapp scattering responsible for the formation of the Mott insulator in the pure case. If it is \ensuremath{\Delta}k=2kF scattering and the disorder is sufficiently weak, the Mott phase survives and the Anderson phase intervenes almost everywhere between the Mott insulator and the conductor, except at one special symmetry-enhanced point corresponding to the fixed commensurate filling: here, as in the pure case, the Mott transition belongs to the Kosterlitz-Thouless universality class. For sufficiently strong disorder, or for any disorder and higher-order scattering, the path from the Mott insulator phase (if it survives) to the conductor always crosses the Anderson phase.
We study the interplay of disorder and interaction effects including bosonic degrees of freedom in the framework of a generic one-dimensional transport model: the Anderson-Edwards model. Using the density-matrix-renormalization group technique, we extract the localization length and the renormalization of the Tomonaga-Luttinger-liquid parameter from the charge-structure factor by a elaborate sample-average finite-size scaling procedure. The properties of the Anderson localized state can be described in terms of scaling relations of the metallic phase without disorder. We analyze how disorder competes with the charge-density-wave correlations triggered by the bosons and give evidence that disorder will destroy the long-range charge-ordered state.
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.