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arXiv:1605.08514 · Physical review. B./Physical review. B

Competition between disorder and Coulomb interaction in a two-dimensional plaquette Hubbard model

Hunpyo Lee, Harald O. Jeschke, Roser Valentí

Published Jun 13, 2016• 17 citations
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Abstract

We have studied a disordered ${N}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{c}}$ plaquette Hubbard model on a two-dimensional square lattice at half-filling using a coherent potential approximation (CPA) in combination with a single-site dynamical mean field theory (DMFT) approach with a paramagnetic bath. Such a model conveniently interpolates between the ionic Hubbard model at ${N}_{\mathrm{c}}=\sqrt{2}$ and the Anderson model at ${N}_{\mathrm{c}}=\ensuremath{\infty}$ and enables the analysis of the various limiting properties. We confirmed that within the CPA approach a band insulator behavior appears for noninteracting strongly disordered systems with a small plaquette size ${N}_{\mathrm{c}}=4$, while the paramagnetic Anderson insulator with nearly gapless density of states is present for large plaquette sizes ${N}_{\mathrm{c}}=48$. When the interaction $U$ is turned on in the strongly fluctuating random potential regions, the electrons on the low energy states push each other into high energy states in DMFT in a paramagnetic bath and correlated metallic states with a quasiparticle peak and Hubbard bands emerge, though a larger critical interaction $U$ is needed to obtain this state from the paramagnetic Anderson insulator (${N}_{\mathrm{c}}=48$) than from the band insulator (${N}_{\mathrm{c}}=4$). Finally, we observe a Mott insulator behavior in the strong interaction $U$ regions for both ${N}_{\mathrm{c}}=4$ and ${N}_{\mathrm{c}}=48$ independent of the disorder strength. We discuss the application of this model to real materials.

DOI
10.1103/physrevb.93.224203

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We have studied a disordered Nc\ifmmode×\else\texttimes\fiNc{N}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{c}}Nc​\ifmmode×\else\texttimes\fiNc​ plaquette Hubbard model on a two-dimensional square lattice at half-filling using a coherent potential approximation (CPA) in combination with a single-site dynamical mean field theory (DMFT) approach with a paramagnetic bath. Such a model conveniently interpolates between the ionic Hubbard model at Nc=2{N}_{\mathrm{c}}=\sqrt{2}Nc​=2​ and the Anderson model at Nc=\ensuremath∞{N}_{\mathrm{c}}=\ensuremath{\infty}Nc​=\ensuremath∞ and enables the analysis of the various limiting properties. We confirmed that within the CPA approach a band insulator behavior appears for noninteracting strongly disordered systems with a small plaquette size Nc=4{N}_{\mathrm{c}}=4Nc​=4, while the paramagnetic Anderson insulator with nearly gapless density of states is present for large plaquette sizes Nc=48{N}_{\mathrm{c}}=48Nc​=48. When the interaction UUU is turned on in the strongly fluctuating random potential regions, the electrons on the low energy states push each other into high energy states in DMFT in a paramagnetic bath and correlated metallic states with a quasiparticle peak and Hubbard bands emerge, though a larger critical interaction UUU is needed to obtain this state from the paramagnetic Anderson insulator (Nc=48{N}_{\mathrm{c}}=48Nc​=48) than from the band insulator (Nc=4{N}_{\mathrm{c}}=4Nc​=4). Finally, we observe a Mott insulator behavior in the strong interaction UUU regions for both Nc=4{N}_{\mathrm{c}}=4Nc​=4 and Nc=48{N}_{\mathrm{c}}=48Nc​=48 independent of the disorder strength. We discuss the application of this model to real materials.
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We study the Anderson-Hubbard model to examine the interplay between the disordered potential and the Hubbard interactions. We use the dynamical mean-field theory (DMFT) with an exact diagonalization as an impurity solver to effectively deal with the quantum fluctuations due to the local interactions. In order to characterize the paramagnetic metal-insulator transition in disordered systems, we compute the typical local density of states, as well as the arithmetically-averaged local density of states. Our approach is found to reproduce the characteristic features of the metal-insulator transition in infinite dimensions, such as the existence of the disorder-driven metallic phase for moderate values of disorder strength and interactions, as observed in earlier studies. In two dimensions, the system turns out to exhibit more insulating behavior when we increase the cluster size in the cellular DMFT. The metallic phase, which is induced from weak Mott insulators by the introduction of a disordered potential, is not observed in two dimensions.
We investigate the effects of Coulomb disorder on the half-filled ionic Hubbard model within the framework of dynamical mean-field theory (DMFT), using the equation-of-motion method as the impurity solver, combined with typical medium theory (TMT). In contrast to conventional disordered Hubbard models, the ionic Hubbard model contains a staggered ionic potential that introduces additional competition between band-insulating and correlation-driven insulating tendencies. We analyze how this ionic potential modifies the electronic phases induced by Coulomb disorder through the arithmetic and geometric averages of the local density of states. In the absence of disorder, the system exhibits metallic (M), Mott-insulating (MI), and band-insulating (BI) phases. When Coulomb disorder is introduced, Anderson-insulating (AI) behavior and localized states (LS) inside the Mott gap are also observed. In particular, the LS regime appears between the metallic and Mott-insulating phases at small ionic potentials, whereas the AI regime develops for sufficiently large values of the Coulomb interaction and ionic potential. Our results show that the interplay between ionic potential, electron correlation, and disorder substantially influences the localization behavior and insulating characteristics of the ionic Hubbard model.
Abstract We study the half-filled Hubbard model with Anderson and Coulomb disorder by mean of dynamical mean field theory using the geometrically averaged local density of states. The paramagnetic phase diagram of the model as a function of the Coulomb interaction and Anderson disorder strength is obtained. The spectral phase diagrams of the ground states for the model are also constructed and discussed. We show that in the intermediate and strong interaction regimes, the Coulomb disorder leads the metallic and Mott insulator phase regions shrink, while the Anderson insulator region is enlarged.
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.
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