Interplay between local response and vertex divergences in many-fermion systems with on-site attraction

Springer, Daniel; Chalupa, P.; Ciuchi, S.; Sangiovanni, Giorgio; Toschi, A.

doi:10.1103/physrevb.101.155148

Cited by 36 publications

(38 citation statements)

References 57 publications

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“…While the self-energy determines the changes of the single-particle excitations due to the mutual interactions, the two-particle correlation functions and collective properties are mostly controlled by the two-particle scattering processes, the so-called vertex correction terms. A dominant role played by the latter clearly emerged from model [19][20][21][22][23][24][25][26][27] and realistic [28][29][30][31][32] calculations of correlated materials. Numerically, the costly parts are the evaluation of the fRG differential flow equations, usually determined by Feynman-type loop diagrams, and the high number of components of the flowing functions such as V (k 1 , k 2 , k 3 , k 4 ).…”

Section: Introductionmentioning

confidence: 99%

Quantitative functional renormalization group description of the two-dimensional Hubbard model

Hille

Kugler

Eckhardt

et al. 2020

Phys. Rev. Research

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Using a leading algorithmic implementation of the functional renormalization group (fRG) for interacting fermions on two-dimensional lattices, we provide a detailed analysis of its quantitative reliability for the Hubbard model. In particular, we show that the recently introduced multiloop extension of the fRG flow equations for the self-energy and two-particle vertex allows for a precise match with the parquet approximation also for twodimensional lattice problems. The refinement with respect to previous fRG-based computation schemes relies on an accurate treatment of the frequency and momentum dependences of the two-particle vertex, which combines a proper inclusion of the high-frequency asymptotics with the so-called truncated unity fRG for the momentum dependence. The adoption of the latter scheme requires, as an essential step, a consistent modification of the flow equation of the self-energy. We quantitatively compare our fRG results for the self-energy and momentumdependent susceptibilities and the corresponding solution of the parquet approximation to determinant quantum Monte Carlo data, demonstrating that the fRG is remarkably accurate up to moderate interaction strengths. The presented methodological improvements illustrate how fRG flows can be brought to a quantitative level for two-dimensional problems, providing a solid basis for the application to more general systems.

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Section: Introductionmentioning

confidence: 99%

Quantitative functional renormalization group description of the two-dimensional Hubbard model

Hille

Kugler

Eckhardt

et al. 2020

Phys. Rev. Research

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“…Such a lack of loop convergence serves as a built-in red-flag indicator that a parameter regime lies outside the zone of safe applicability of the approach. This outcome, however, is not entirely unexpected since, for the specific AIM considered, the interaction strength U = 3 already corresponds to the strong-coupling regime, where nonperturbative [50,[68][69][70] divergences of two-particle irreducible vertices [71][72][73][74][75][76][77][78], which are-per construction-beyond the PA, were detected by means of QMC calculations [50,59]. More speculatively, one might then suppose a relation between the breakdown of the mfRG convergence and the entrance into the nonperturbative parameter regime, where the PA itself yields results significantly different from the exact solution [50].…”

Section: B Towards Strong Couplingmentioning

confidence: 79%

Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model

Chalupa-Gantner,

Kugler,

Hille

et al. 2021

Preprint

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We investigate several fundamental characteristics of the multiloop functional renormalization group (mfRG) flow by hands of its application to a prototypical many-electron system: the Anderson impurity model (AIM).We first analyze the convergence of the algorithm in the different parameter regions of the AIM. As no additional approximation is made, the multiloop series for the local self-energy and response functions converge perfectly to the corresponding results of the parquet approximation (PA) in the weak-to intermediate-coupling regime. Small oscillations of the mfRG solution as a function of the loop order gradually increase with the interaction, hindering a full convergence to the PA in the strong-coupling regime, where perturbative resummation schemes are no longer reliable. By exploiting the converged results, we inspect the fulfillment of (i) sum rules associated to the Pauli principle and (ii) Ward identities related to conservation laws. For the Pauli principle, we observe a systematic improvement by increasing the loop order and including the multiloop corrections to the self-energy. This is consistent with the preservation of crossing symmetries and two-particle self-consistency in the PA. For the Ward identities, we numerically confirm a visible improvement by means of the Katanin substitution. At weak coupling, violations of the Ward identity are further reduced by increasing the loop order in mfRG. For larger interaction values, the overall behavior becomes more complex, and the benefits of the higher-loop terms are mostly present in the contributions at large frequencies.

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“…Ref. [23] of the paper. The odd in frequency eigenfunctions may however play important role in description of screening of local magnetic moment, see Sect.…”

Section: Eigenvalues Of Charge Susceptibilitymentioning

confidence: 99%

“…[12,16]). The developments of the non-local diagrammatic extensions of DMFT [17] yielded a new insight on the non-perturbative aspects of Mott transition via studying the divergences of the two-particle irreducible vertices [18][19][20][21][22][23][24]. These divergences were interpreted as the precursors of local moment formation [22,25].…”

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confidence: 99%

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Local magnetic moment formation and Kondo screening in the half filled two dimensional single band Hubbard model

Mazitov,

Katanin

2021

Preprint

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Interplay between local response and vertex divergences in many-fermion systems with on-site attraction

Cited by 36 publications

References 57 publications

Quantitative functional renormalization group description of the two-dimensional Hubbard model

Quantitative functional renormalization group description of the two-dimensional Hubbard model

Fulfillment of sum rules and Ward identities in the multiloop functional renormalization group solution of the Anderson impurity model

Local magnetic moment formation and Kondo screening in the half filled two dimensional single band Hubbard model

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