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arXiv:1806.07969 · Physical review. B./Physical review. B

Strong-coupling perturbative study of the disordered Hubbard model on the honeycomb lattice

Alireza Habibi, Elaheh Adibi, Somaye Jafari

Published Dec 3, 2018• 5 citations
arXivHTMLPDF

Abstract

We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is handled with strong-coupling perturbation theory which encodes the information about Mott transition physics into a rich dynamical local self-energy. The local nature of the self-energy allows us to combine it with kernel polynomial and transfer matrix methods which consequently enables us to study lattices with millions of sites. The transfer matrix method, which in the ribbon geometry is essentially free from finite-size errors, can be employed to perform finite-size scaling on the width of the ribbon. This enables us to rule out the possibility of metallic phase between the Mott and Anderson insulating phases which has been claimed in the literature. Therefore, we find a direct transition between Anderson and Mott insulators when the disorder strength $W$ is comparable to the Hubbard interaction $U$. For a fixed disorder strength $W$, we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions $U$, the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.

DOI
10.1103/physrevb.98.245105

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We study the Anderson disordered Hubbard model on the honeycomb lattice. The Hubbard term is handled with strong-coupling perturbation theory which encodes the information about Mott transition physics into a rich dynamical local self-energy. The local nature of the self-energy allows us to combine it with kernel polynomial and transfer matrix methods which consequently enables us to study lattices with millions of sites. The transfer matrix method, which in the ribbon geometry is essentially free from finite-size errors, can be employed to perform finite-size scaling on the width of the ribbon. This enables us to rule out the possibility of metallic phase between the Mott and Anderson insulating phases which has been claimed in the literature. Therefore, we find a direct transition between Anderson and Mott insulators when the disorder strength WWW is comparable to the Hubbard interaction UUU. For a fixed disorder strength WWW, we obtain an interaction-dependent nonmonotonic behavior of the localization length which reflects the interaction-induced enhancement of the localization length for weak and intermediate interaction strengths. Eventually, at strong interactions UUU, the Mott localization takes over, and the localization length becomes comparable to the lattice scale. This phenomenon is reminiscent of the holographic determination of the Mott state where the system at infrared recognizes its ultraviolet lattice scale.
In the binary alloy with composition ${A}_{x}{B}_{1\ensuremath{-}x}$ of two atoms with ionic energy scales $\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{\Delta}}$, an apparent Anderson insulator (AI) is obtained as a result of randomness in the position of atoms. Using our recently developed technique that combines the local self-energy from strong-coupling perturbation theory with the transfer matrix method, we are able to address the problem of adding a Hubbard UUU to the binary-alloy problem for millions of lattice sites on the honeycomb lattice. By adding the Hubbard interaction UUU, the resulting AI phase will become metallic, which in our formulation can be manifestly attributed to the screening of disorder by Hubbard UUU. Upon further increase in UUU, again the AI phase emerges, which can be understood in terms of the suppressed charge fluctuations due to residual Hubbard interaction. The randomness takes advantage of such suppression and localizes the quasiparticles of the metallic phase. The ultimate destiny of the system at very large UUU is to become a Mott insulator. We construct the phase diagram of this model in the plane of $(U,\mathrm{\ensuremath{\Delta}})$ for various compositions xxx.
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 derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.
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 UUU there is re-entrant behavior from the Anderson localized phase to the metallic phase.
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.
The DOS, the dynamic (optical) conductivity, and the phase diagram of a strongly correlated and strongly disordered paramagnetic Anderson-Hubbard model are analyzed within the generalized dynamical mean field theory (DMFT + Σ approximation). Strong correlations are taken into account by the DMFT, and disorder is taken into account via an appropriate generalization of the self-consistent theory of localization. The DMFT effective single-impurity problem is solved by a numerical renormalization group (NRG); we consider the three-dimensional system with a semielliptic DOS. The correlated metal, Mott insulator, and correlated Anderson insulator phases are identified via the evolution of the DOS and dynamic conductivity, demonstrating both the Mott-Hubbard and Anderson metal-insulator transition and allowing the construction of the complete zero-temperature phase diagram of the Anderson-Hubbard model. Rather unusual is the possibility of a disorder-induced Mott insulator-to-metal transition.