Long-Range Coulomb Interactions in Surface Systems: A First-Principles Description within Self-Consistently Combined<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:math>and Dynamical Mean-Field Theory

Hansmann, P.; Ayral, Thomas; Vaugier, Loïg; Werner, Philipp; Biermann, Silke

doi:10.1103/physrevlett.110.166401

Cited by 119 publications

(178 citation statements)

References 48 publications

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“…In fact, the results obtained in the simplified "dual" approaches that include at least the electron-boson vertex γ are similar to those obtained by the GW +EDMFT method, which is conceptually and practically simpler than dual methods and has hence already been applied to realistic materials in a number of works [53][54][55][56].…”

Section: Beyond Gw+edmft: Comparison To Dual Bosons and Trilexsupporting

confidence: 55%

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

et al. 2017

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In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a bandwidening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and GW +EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in GW +EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex. DOI: 10.1103/PhysRevB.95.245130 Dynamical mean field theory (DMFT) [1] self-consistently maps a correlated Hubbard lattice problem with local interactions onto an effective impurity problem consisting of a correlated orbital hybridized with a noninteracting fermionic bath. If the bath is integrated out, one obtains an impurity action with retarded hoppings. Extended dynamical mean field theory [2-10] (EDMFT) extends the DMFT idea to systems with long-range interactions. It does so by mapping a lattice problem with long-range interactions onto an effective impurity model with self-consistently determined fermionic and bosonic baths, or, in the action formulation, an impurity model with retarded hoppings and retarded interactions.While EDMFT captures dynamical screening effects and charge-order instabilities, it has been found to suffer from qualitative shortcomings in finite dimensions. For example, the charge susceptibility computed in EDMFT does not coincide with the derivative of the average charge with respect to a small applied field [11], nor does it obey local charge conservation rules [12] essential for an adequate description of collective modes such as plasmons.The EDMFT formalism has an even more basic deficiency: since it is based on a local approximation to the self-energy, it does not include even the first-order nonlocal interaction term, the Fock term. The combined GW +EDMFT [13][14][15] scheme corrects this by supplementing the local self-energy from EDMFT with the nonlocal part of the GW diagram, where G is the interacting Green's function and W the fully screened interaction. Indeed, the nonlocal Fock term [Gv] nonloc is included in the nonlocal [GW ] nonloc diagram. As described in more detail in Ref. [15] (see also the appendix of Ref.[16]), the GW +EDMFT method is formally obtained by constructing an energy functional of G and W , the Almbladh [17] functional , and by approximating as a sum of two terms, one containing all local diagrams (corresponding to EDMFT) and the other containing the simplest nonlocal correction (corresponding to the GW approximation [18]). This functional construct...

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Section: Beyond Gw+edmft: Comparison To Dual Bosons and Trilexsupporting

confidence: 55%

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

et al. 2017

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“…One strategy, which has been recently explored in simple model contexts [15][16][17], is to combine the local DMFT self-energy with the nonlocal component of some manybody perturbation theory (MBPT) such as second-order * Corresponding author: gukelberger@phys.ethz.ch weak-coupling perturbation theory ( (2) ) or the GW [18] approximation [19,20]. Alternative schemes, such as the combination with the nonlocal self-energy from the fluctuationexchange approximation (FLEX) [21,22] or the T -matrix approximation (TMA) [23], will also be considered in this work.…”

Section: Introductionmentioning

confidence: 99%

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

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We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second-order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW + DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second-order diagram. FLEX + DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

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“…While this GW + EDMFT formalism has been tested on simple one-band Hubbard models [14][15][16][17], and several simplified versions have been applied to SrVO 3 [7,10,18,19], a fully self-consistent implementation in an ab initio setting has so far been hampered by the challenges of solving the bosonic selfconsistency loop for multiorbital systems and nontrivial issues related to a proper embedding of the EDMFT calculations into a GW ab initio framework.…”

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confidence: 99%

When strong correlations become weak: Consistent merging of GW and DMFT

Boehnke¹,

Nilsson²,

et al. 2016

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The cubic perovskite SrVO 3 is generally considered to be a prototype strongly correlated metal with a characteristic three-peak structure of the d-electron spectral function, featuring a renormalized quasiparticle band in between pronounced Hubbard sidebands. Here we show that this interpretation, which has been supported by numerous "ab initio" simulations, has to be reconsidered. Using a fully self-consistent GW + extended dynamical mean-field theory calculation we find that the screening from nonlocal Coulomb interactions substantially reduces the effective local Coulomb repulsion, and at the same time leads to strong plasmonic effects. The resulting effective local interactions are too weak to produce pronounced Hubbard bands in the local spectral function, while prominent plasmon satellites appear at energies which agree with those of the experimentally observed sidebands. Our results demonstrate the important role of nonlocal interactions and dynamical screening in determining the effective interaction strength of correlated compounds. DOI: 10.1103/PhysRevB.94.201106 SrVO 3 has been considered a prototype strongly correlated metal ever since photoemission and inverse photoemission experiments 20 years ago [1] showed features at energies well outside the renormalized quasiparticle band. These satellites have been explained as Hubbard bands, because they appear in combined density functional + dynamical mean-field theory (LDA+DMFT) [2] simulations when the local Coulomb repulsion is chosen such that the experimentally observed mass renormalization is reproduced (see, e.g., Refs. [3][4][5]). Comparable values for the "Hubbard U " on the order of 5 eV were obtained by constrained local density approximation (LDA) [6,7] and used in DMFT calculations with static local interactions. The constrained random phase approximation (cRPA) [8] provides a systematic way of computing the dynamically screened interaction parameters consistent with the LDA band structure, and the resulting local U (ω) of the DMFT auxiliary system can be efficiently handled by state-of-the-art impurity solvers [9]. These more realistic calculations, however, produce a too strong renormalization of the quasiparticle band [10]. The missing ingredients in the LDA+DMFT + U (ω) approach are the nonlocal self-energy and polarization effects, and the additional screening of the U (ω) resulting from nonlocal Coulomb interactions within the low-energy subspace.A promising scheme, which can treat all these effects in a consistent manner, is the combination of the GW ab initio method [11] and extended DMFT (EDMFT) [12,13]. While this GW + EDMFT formalism has been tested on simple one-band Hubbard models [14][15][16][17], and several simplified versions have been applied to SrVO 3 [7,10,18,19], a fully self-consistent implementation in an ab initio setting has so far been hampered by the challenges of solving the bosonic selfconsistency loop for multiorbital systems and nontrivial issues related to a proper embedding of the EDMFT calculations into a ...

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Long-Range Coulomb Interactions in Surface Systems: A First-Principles Description within Self-Consistently CombinedGWand Dynamical Mean-Field Theory

Cited by 119 publications

References 48 publications

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

When strong correlations become weak: Consistent merging of GW and DMFT

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