We derive an analytical expression for the local two-particle vertex of the Falicov-Kimball model, including its dependence on all three frequencies, the full vertex, and all reducible vertices. This ...allows us to calculate the self-energy in diagrammatic extensions of dynamical mean field theory, specifically in the dual fermion and the one-particle irreducible approach. Nonlocal correlations are thence included and originate here from charge-density wave fluctuations. At low temperatures and in two dimensions, they lead to a larger self-energy contribution at low frequencies and a more insulating spectrum.
The parquet decomposition of the self-energy into classes of diagrams, those associated with specific scattering processes, can be exploited for different scopes. In this work, the parquet ...decomposition is used to unravel the underlying physics of nonperturbative numerical calculations. We show the specific example of dynamical mean field theory and its cluster extensions dynamical cluster approximation (DCA) applied to the Hubbard model at half-filling and with hole doping: These techniques allow for a simultaneous determination of two-particle vertex functions and self-energies and, hence, for an essentially "exact" parquet decomposition at the single-site or at the cluster level. Our calculations show that the self-energies in the underdoped regime are dominated by spin-scattering processes, consistent with the conclusions obtained by means of the fluctuation diagnostics approach O. Gunnarsson et al., Phys. Rev. Lett. 114, 236402 (2015). However, differently from the latter approach, the parquet procedure displays important changes with increasing interaction: Even for relatively moderate couplings, well before the Mott transition, singularities appear in different terms, with the notable exception of the predominant spin channel. We explain precisely how these singularities, which partly limit the utility of the parquet decomposition and, more generally, of parquet-based algorithms, are never found in the fluctuation diagnostics procedure. Finally, by a more refined analysis, we link the occurrence of the parquet singularities in our calculations to a progressive suppression of charge fluctuations and the formation of a resonance valence bond state, which are typical hallmarks of a pseudogap state in DCA.
We have studied the impact of nonlocal electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining ...dynamical vertex approximation, lattice quantum Monte Carlo, and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling, irrespective of the preformation of localized or short-range magnetic moments. This is the reason why the two-dimensional Hubbard model has a paramagnetic phase which is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.
We have implemented the dynamical vertex approximation (DGammaA) in its full parquet-based version to include spatial correlations on all length scales and in all scattering channels. The algorithm ...is applied to study the electronic self-energies and the spectral properties of finite-size one-dimensional Hubbard models with periodic boundary conditions (nanoscopic Hubbard rings). From a methodological point of view, our calculations and their comparison to the results obtained within dynamical mean-field theory, plain parquet approximation, and the exact numerical solution allow us to evaluate the performance of the DGammaA algorithm in the most challenging situation of low dimensions. From a physical perspective, our results unveil how nonlocal correlations affect the spectral properties of nanoscopic systems of various sizes in different regimes of interaction strength.
Local n-particle vertex functions represent the crucial ingredient for diagrammatic extensions of dynamical mean field theory (DMFT). Hitherto their application has been restricted-with a few ...exceptions-to the n=2-particle vertex while higher-order vertices have been neglected. In this paper we derive a general analytical expression for the local n-particle (one-particle-reducible) vertex of the Falicov-Kimball model (FKM). We observe that the magnitude of such vertex functions itself strongly increases with the number of particles n. On the other hand, their effect on generic Feynman diagrams remains rather moderate due to the damping effect of the Green's functions present in such diagrams. Nevertheless, they yield important contributions to the self-energy corrections calculated in diagrammatic extensions of DMFT as we explicitly demonstrate using the example of dual-fermion calculations for the two-dimensional FKM at quarter filling of the stationary f electrons. Here corrections to the self-energy obtained from the three-particle vertex are indeed comparable in magnitude to corresponding corrections stemming from the two-particle vertex.
We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper O. Gunnarsson et al., Phys. Rev. ...Lett. 114, 236402 (2015), we introduced the “fluctuation diagnostics” approach to extract the dominant wave-vector-dependent bosonic fluctuations from the electronic self-energy. Here, we first reformulate the theory in terms of fermionic modes to render its connection with resonance valence bond (RVB) fluctuations more transparent. Second, by using a large-U expansion, where U is the Coulomb interaction, we relate the fluctuations to real-space correlations. Therefore, it becomes possible to study how electron spectra are related to charge, spin, superconductivity, and RVB-like real-space correlations, broadening the analysis of an earlier work J. Merino and O. Gunnarsson, Phys. Rev. B 89, 245130 (2014). This formalism is applied to the pseudogap physics of the two-dimensional Hubbard model, studied in the dynamical cluster approximation. We perform calculations for embedded clusters with up to 32 sites, having three inequivalent K points at the Fermi surface. We find that as U is increased, correlation functions gradually attain values consistent with an RVB state. This first happens for correlation functions involving the antinodal point and gradually spreads to the nodal point along the Fermi surface. Simultaneously, a pseudogap opens up along the Fermi surface. We relate this to a crossover from a Kondo-type state to an RVB-like localized cluster state and to the presence of RVB and spin fluctuations. These changes are caused by a strong momentum dependence in the cluster bath couplings along the Fermi surface. We also show, from a more algorithmic perspective, how the time-consuming calculations in fluctuation diagnostics can be drastically simplified.
We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb ...interaction. It includes the so‐called GW and dynamical mean field theory and important non‐local correlations beyond, with a computational effort estimated to be still manageable.
The authors propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so‐called GW and dynamical mean field theory and important non‐local correlations beyond, with a computational effort estimated to be still manageable.
The optical conductivity σ(ω) and the spectral weight W(T) of two superconducting cuprates at optimum doping, Bi2Sr2-xLaxCuO6 and Bi2Sr2CaCu2O8, have been first measured up to 500 K. Above 300 K, ...W(T) deviates from the usual T2 behavior in both compounds, even though σ(ω→0) remains larger than the Ioffe-Regel limit. The deviation is surprisingly well described by the T4 term of the Sommerfeld expansion, but its coefficients are enhanced by strong correlation, as shown by the good agreement with dynamical mean field calculations.
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