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

Ayral, Thomas; Biermann, Silke; Werner, Philipp; Boehnke, Lewin

doi:10.1103/physrevb.95.245130

Cited by 61 publications

(64 citation statements)

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“…However, an account for vertex corrections beyond the dynamical mean-field solution is desirable [66][67][68]. Especially, it is an important problem for description of spin fluctuations and magnetic polarization in realistic systems [69,70] as they are not captured by a standard GW+DMFT scheme [35][36][37][38][39][40][41]. While the use of the fermion-boson vertex in a diagrammatic solution of multiband problems is possible [44], an inclusion of the fermion-fermion vertex in realistic calculations is extremely challenging and time consuming numerically [29][30][31][32][33][34].…”

Section: B Collective Electronic Effects Beyond Edmftmentioning

confidence: 99%

Consistent partial bosonization of the extended Hubbard model

2019

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We design an efficient and balanced approach that captures major effects of collective electronic fluctuations in strongly correlated fermionic systems using a simple diagrammatic expansion on a basis of dynamical meanfield theory. For this aim we perform a partial bosonization of collective fermionic fluctuations in leading channels of instability. We show that a simultaneous account for different bosonic channels can be done in a consistent way that allows to avoid the famous Fierz ambiguity problem. The present method significantly improves a description of an effective screened interaction W in both, charge and spin channels, and has a great potential for application to realistic GW-like calculations for magnetic materials.

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Section: B Collective Electronic Effects Beyond Edmftmentioning

confidence: 99%

Consistent partial bosonization of the extended Hubbard model

2019

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“…This can be understood by noticing that α = 0.5 corresponds to the values of U η used in the random phase approximation (RPA), which is correct to second order in U . Moreover, we compare our results with the self-energy obtained by the GW +EDMFT [60][61][62][63][64][65][66] method for N c = 4. GW +EDMFT can be regarded as a simplification of TRILEX where the vertex corrections are neglected in the nonlocal self-energy contribution.…”

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confidence: 99%

Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters

2017

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We present an embedded-cluster method, based on the TRILEX formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, selfenergies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the GW +extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.Two major approaches have been put forth to fathom the nature of high-temperature superconductivity. Spin fluctuation theory [1][2][3][4][5][6][7][8] , inspired by the early experiments on cuprate compounds, is based on the introduction of phenomenological bosonic fluctuations coupled to the electrons. It belongs to a larger class of methods, including the fluctuation-exchange (FLEX) 9 and GW approximations 10,11 , or the Eliashberg theory of superconductivity 12 . In the Hubbard model, these methods can formally be obtained by decoupling the electronic interactions with Hubbard-Stratonovich (HS) bosons carrying charge, spin or pairing fluctuations. They are particularly well suited for describing the system's long-range modes. However, they suffer from two main drawbacks: without an analog of Migdal's theorem for spin fluctuations, they are quantitatively uncontrolled; worse, the results depend on the precise form of the bosonic fluctuations used to decouple the interaction term, an issue referred to as the "Fierz ambiguity" [13][14][15][16][17][18] .A second class of methods, following Anderson 19 , puts primary emphasis on the fact that the undoped compounds are Mott insulators, where local physics plays a central role. Approaches like dynamical mean field theory (DMFT) 20 and its cluster extensions 21-25 , which self-consistently map the lattice problem onto an effective problem describing a cluster of interacting atoms embedded in a noninteracting host, are tools of choice to examine Anderson's idea. Cluster DMFT has indeed been shown to give a consistent qualitative picture of cuprate physics, including pseudogap and superconducting phases . Compared to fluctuation theories, it a priori comes with a control parameter, the size N c of the embedded cluster. However, this is of limited practical use, since the convergence with N c is nonmonotonic for small N c 33 , requiring large N c 's, which cann...

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“…The actual GW +EDMFT results roughly follow the [46]. In the current study, we restrict our discussion to the metallic phase.…”

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confidence: 55%

Nonlocal Coulomb interaction and spin-freezing crossover as a route to valence-skipping charge order

et al. 2020

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Multiorbital systems away from global half-filling host intriguing physical properties promoted by Hund's coupling. Despite increasing awareness of this regime dubbed Hund's metal, effect of nonlocal interaction is still elusive. Here we study a three-orbital model with 1/3 filling (two electrons per site) including the intersite Coulomb interaction (V ). Using the GW plus extended dynamical mean-field theory, the valence-skipping charge order transition is shown to be driven by V . Most interestingly, the instability to this transition is significantly enhanced in the spin-freezing crossover regime, thereby lowering the critical V to the formation of charge order. This behavior is found to be closely related to the population profile of the atomic multiplet states in the spin-freezing regime. In this regime, maximum spin states are dominant in each total charge subspace with substantial amount of one-and three-electron occupations, which leads to almost equal population of one-and the maximum spin three-electron state. Our finding unveils another feature of the Hund's metal, and has potential implications to the broad range of multiorbital systems as well as the recently discovered charge order in iron-pnictides.Classifying a number of phases and understanding their relevance to different energy scales has been a central theme of condensed matter physics. In multiorbital systems away from global half-filling, Hund's coupling was shown to promote a bad metallic behavior while simultaneously pushing away the Mott insulating region [1-3]. The term Hund's metal [4,5] was coined to classify the regime in which the "Hundness" not the "Mottness" plays a leading role in determining physical properties [6,7]. The Hund's metal hosts rich phenomena such as finite temperature spin-freezing crossover [7-9], spin-orbital separation [7,10,11], anomalous transport behavior [3,4,8], increased electronic compressibility [12,13], and the orbital-differentiation [2,[14][15][16][17]. It has been believed to be one of the central doctrines to understand the intriguing physics of (mainly, but not limited to) iron-based superconductors [3-5, 12-15, 18-20] and ruthenates [3,8,21,22].In addition to the above mentioned direct manifestations of Hund's metal regime, its connection and proximity to the symmetry-broken charge-disproportionated phases has recently been highlighted [23,24]. Those which are called Hund's insulator [23] and valenceskipping phase [24-26] -a phase with two different valences while skipping the intermediate one between the two -are prominent examples. One possible route to the valence-skipping is the negative effective Coulomb repulsion, U eff < 0 [24,27,28]. Interestingly, a purely intraatomic origin, namely the anisotropic orbital-multipole scattering, was suggested to be the key ingredient for such valence-skipping phenomena [24]. Furthermore, this phase has potential implications to the electron pairing mechanisms of unconventional superconductivity [24,29].The valence-skipping compounds are prevalent in Na-tur...

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

Cited by 61 publications

References 62 publications

Consistent partial bosonization of the extended Hubbard model

Consistent partial bosonization of the extended Hubbard model

Fierz Convergence Criterion: A Controlled Approach to Strongly Interacting Systems with Small Embedded Clusters

Nonlocal Coulomb interaction and spin-freezing crossover as a route to valence-skipping charge order

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