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arXiv:1205.5553 · Physical Review Letters

Spectral Properties of Correlated Materials: Local Vertex and Nonlocal Two-Particle Correlations from Combined G W and Dynamical Mean Field Theory

Thomas Ayral, Philipp Werner, Silke Biermann

Published Nov 28, 2012• 94 citations
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Abstract

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.

DOI
10.1103/physrevlett.109.226401

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We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.
We combine the single-site dynamical mean field theory (DMFT) with the non-local GW method. This is done fully self-consistently and we apply our formalism to a one-band Hubbard model. Eventually at self-consistency the full self-energy and polarization operator of the system are retrieved. Some numerical results, in the metallic as well as the insulator regime, are presented and briefly discussed. Depending on the involved interaction (GW) parameters, substantial changes are found when the GW self-energy is incorporated. However, the main point of this work is to demonstrate the applicability of the method, not to make any strict comparison with exact results and experiments.
Nonlocal correlations play an essential role in correlated electron systems, especially in the vicinity of phase transitions and crossovers, where two-particle correlation functions display a distinct momentum dependence. In nonequilibrium settings, the effect of nonlocal correlations on dynamical phase transitions, prethermalization phenomena, and trapping in metastable states is not well understood. In this paper, we introduce a dynamical mean field theory (DMFT) extension to the nonequilibrium two-particle self-consistent (TPSC) approach, which allows to perform nonequilibrium simulations capturing short- and long-ranged nonlocal correlations in the weak-, intermediate-, and strong-correlation regimes. The method self-consistently computes local spin and charge vertices, from which a momentum-dependent self-energy is constructed. Replacing the local part of the self-energy by the DMFT result within this self-consistent scheme provides an improved description of local correlation effects. We explain the details of the formalism and the implementation, and demonstrate the versatility of DMFT+TPSC with interaction quenches and dimensional crossovers in the Hubbard model.
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Using extended dynamical mean-field theory and its combination with the GWGWGW 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.