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arXiv:1404.7047 · Physical Review B

Extended dynamical mean-field study of the Hubbard model with long-range interactions

Li Huang, Thomas Ayral, Silke Biermann, Philipp Werner

Published Nov 10, 2014• 85 citations
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Abstract

Using extended dynamical mean-field theory and its combination with the $GW$ approximation, we compute the phase diagrams and local spectral functions of the single-band extended Hubbard model on the square and simple cubic lattices, considering long-range interactions up to the third nearest neighbors. The longer-range interactions shift the boundaries between the metallic, charge-ordered insulating, and Mott insulating phases, and lead to characteristic changes in the screening modes and local spectral functions. Momentum-dependent self-energy contributions enhance the correlation effects and thus compete with the additional screening effect from longer-range Coulomb interactions. Our results suggest that the influence of longer-range intersite interactions is significant, and that these effects deserve attention in realistic studies of correlated materials.

DOI
10.1103/physrevb.90.195114

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We study the half-filled extended Hubbard model on a two-dimensional square lattice using cluster dynamical mean-field theory on clusters of size 8--20. We show that the model exhibits metallic, Mott-insulating, and charge-ordered phases, and determine the location of the charge-ordering phase-transition line and the properties of the phases as a function of temperature, local interaction, and nearest-neighbor interaction. We find strong nonlocal correlations outside the charge-ordered phase and a pronounced screening effect in the vicinity of the phase transition, where nonlocal interactions push the system towards metallic behavior. In contrast, correlations in the charge-ordered phase are mostly local to the unit cell. Finally, we demonstrate how strong nonlocal electron-electron interactions can increase electron mobility by turning a charge-ordered insulator into a metal. We analyze finite-size effects and the convergence of our data to the thermodynamic limit. Control of all sources of errors allows us to assess the regime of applicability of simpler approximation schemes for systems with nonlocal interactions.
We provide solid evidence for the long-standing presumption that model Hamiltonians with short-range interactions faithfully reproduce the physics of the long-range Coulomb interaction in real materials. For this aim, we address a generic Hubbard model that captures the quantum phase transitions between metal, Mott insulator, and charge-density-wave (CDW) insulator, in the absence of Fermi-surface nesting. By comparing the quantum phase diagrams for the 1 / r -Hubbard model on a half-filled chain with nearest-neighbor and 1 / r -long-range interactions, we argue that the inclusion of long-range interactions is not crucial for a proper description of interacting many-electron systems. To this end, we employ the density matrix renormalization group method on finite lattices and antiperiodic boundary conditions to determine the quantum phase transitions between the metallic Luttinger liquid for weak interactions, the Mott-Hubbard insulator for dominant on-site interactions, and the CDW insulator for dominant intersite interactions. The two phase diagrams qualitatively agree inasmuch as the quantum phase transitions are continuous in both cases. Moreover, simple Hartree-Fock theory and the atomic limit provide renormalization factors that allow us to quantitatively map the two phase diagrams onto each other. As a practical advantage, our findings imply that computational efforts can be reduced tremendously by using models with short-range interactions only.
We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\ifmmode\times\else\texttimes\fi{}2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction VVV causes ``screening'' effects close to the Mott phase transition, pushing the phase boundary to larger values of UUU. We also demonstrate the different effects of VVV on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.
We present a fully self-consistent combined GW and dynamical mean field (DMFT) study of the extended two-dimensional Hubbard model. The inclusion of the local dynamical vertex stemming from the DMFT self-energy and polarization is shown to cure the known problems of self-consistent GW. We calculate momentum-resolved spectral functions, two-particle polarizations, and electron-loss spectra, as well as the effective dynamical interaction induced by nonlocal screening. The momentum-dependence introduced by GW into the extended DMFT description leads to a narrowing of the quasiparticle width and more pronounced Hubbard bands in the metallic regime as one approaches the charge-ordering transition. It further affects the shape of collective modes, giving rise to dispersive plasmon-like long-wavelength and stripe modes.
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