Local electronic correlation at the two-particle level

Rohringer, G.; Valli, Angelo; Toschi, A.

doi:10.1103/physrevb.86.125114

Cited by 204 publications

(385 citation statements)

References 105 publications

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“…The reason for this is that the U appearing in the D A equation (37) is replaced by the irreducible vertex in the 1PI formula. At small values of the interaction parameter U , the (irreducible) vertex is smaller 9,32 than the bare interaction due to metallic screening. Therefore, nonlocal corrections obtained within the 1PI formalism tend to be smaller than the one obtained in D A.…”

Section: A One-shot Calculationsmentioning

confidence: 99%

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One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

et al. 2013

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We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length scales beyond the local correlations of dynamical mean-field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D A) and the dual fermion (DF) scheme, yielding a consistent formulation of nonlocal correlations at the one-and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three-and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D A. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF, and D A, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.

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Section: A One-shot Calculationsmentioning

confidence: 99%

“…Here, the local (irreducible) vertex is strongly enhanced 9,32,33 compared to the bare Hubbard interaction U , due to the formation of the local moment …”

Section: A One-shot Calculationsmentioning

confidence: 99%

One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

et al. 2013

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“…In standard DMFT applications typically one-particle (1P) quantities such as the self-energy and the spectral function allow for a clear-cut identification of the boundaries of the first-order Mott-Hubbard transition [42][43][44] . Here, however, we will focus mainly on the DMFT analysis of local two-particle (2P) correlation functions, whose behavior is also strongly affected by the Mott transition [45][46][47] . Hence, in the following, we will recapitulate in Sec.…”

Section: A Choice Of Parametersmentioning

confidence: 99%

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

et al. 2016

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We analyze the highly non-perturbative regime surrounding the Mott-Hubbard metal-to-insulator transition (MIT) by means of dynamical mean field theory (DMFT) calculations at the two-particle level. By extending the results of Schäfer, et al. [Phys. Rev. Lett. 110, 246405 (2013)] we show the existence of infinitely many lines in the phase diagram of the Hubbard model where the local Bethe-Salpeter equations, and the related irreducible vertex functions, become singular in the charge as well as the particle-particle channel. By comparing our numerical data for the Hubbard model with analytical calculations for exactly solvable systems of increasing complexity [disordered binary mixture (BM), Falicov-Kimball (FK) and atomic limit (AL)], we have (i) identified two different kinds of divergence lines; (ii) classified them in terms of the frequency-structure of the associated singular eigenvectors; (iii) investigated their relation to the emergence of multiple branches in the Luttinger-Ward functional. In this way, we could distinguish the situations where the multiple divergences simply reflect the emergence of an underlying, single energy scale ν * below which perturbation theory is no longer applicable, from those where the breakdown of perturbation theory affects, not trivially, different energy regimes. Finally, we discuss the implications of our results on the theoretical understanding of the non-perturbative physics around the MIT and for future developments of many-body algorithms applicable in this regime.

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“…We include correlations on all length scales by either extrapolating lattice BSS-QMC results to N c → ∞ or using DΓA [35] in its ladder version [41], a diagrammatic extension of DMFT (cf. [38,48,49]) based on the two-particle vertex [50,51]. Certainly, both approaches have their limitations, either due to the extrapolation procedure of the cluster results (see Supplement) or due to the selection of the more relevant subsets of diagrams.…”

Section: Introductionmentioning

confidence: 99%

Fate of the false Mott-Hubbard transition in two dimensions

et al. 2015

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We have studied the impact of non-local electronic correlations at all length scales on the MottHubbard 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 -irrespectively of the preformation of localized or short-ranged 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. Introduction.The Mott-Hubbard metal-insulator transition (MIT) [1] is one of the most fundamental hallmarks of the physics of electronic correlations. Nonetheless, astonishingly little is known exactly, even for its simplest modeling, i.e., the single-band Hubbard Hamiltonian [2]: Exact solutions for this model are available only in the extreme, limiting cases of one and infinite dimensions.In one dimension (1D), the Bethe ansatz shows that there is actually no Mott-Hubbard transition [3][4][5]; or, in other words, it occurs for a vanishingly small Hubbard interaction U : At any U > 0 the 1D-Hubbard model is insulating at half filling. One dimension is, however, rather peculiar: While there is no antiferromagnetic ordering even at temperature T = 0, antiferromagnetic spin fluctuations are strong and long-ranged, decaying slowly, i.e., algebraically. Also the (doped) metallic phase is not a standard Fermi liquid but a Luttinger liquid.For the opposite extreme, infinite dimensions, the dynamical mean field theory (DMFT) [6] becomes exact [7], which allows for a clear-cut and -to a certain extentalmost "idealized" description of a pure Mott-Hubbard MIT. In fact, since in D = ∞ only local correlations survive [7], the Mott-Hubbard insulator of DMFT consists of a collection of localized (but not long-range ordered) magnetic moments. This way, if antiferromagnetic order is neglected or sufficiently suppressed, DMFT describes a first-order MIT [6,8], ending with a critical endpoint.As an approximation, DMFT is applicable to the more realistic cases of the three-and two-dimensional Hubbard models. However, the DMFT description of the MIT is the very same here, since only the non-interacting density of states (DOS) and in particular its second moment enter. This is a natural shortcoming of the mean-field nature of DMFT: antiferromagnetic fluctuations have no effect at all on the DMFT spectral function or self-energy above the antiferromagnetic ordering temperature T N .In 3D, antiferromagnetic fluctuations reduce T N siz-

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Local electronic correlation at the two-particle level

Cited by 204 publications

References 105 publications

One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

Nonperturbative landscape of the Mott-Hubbard transition: Multiple divergence lines around the critical endpoint

Fate of the false Mott-Hubbard transition in two dimensions

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