Parquet approximation for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>4</mml:mn><mml:mo>×</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:math>Hubbard cluster

Yang, Shuxiang; Fotso, Herbert; Li, Jun; Maier, Thomas; Tomko, Karen; D’Azevedo, E.; Scalettar, Richard; Pruschke, Thomas; Jarrell, Mark

doi:10.1103/physreve.80.046706

Cited by 74 publications

(89 citation statements)

References 13 publications

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“…The specific parameters in Eq. (12) have been chosen in this case as follows: n = 1 (half-filling) and β = 26 eV −1 . The results of the parquet decomposition of the DMFT self-energy are shown in Fig.…”

Section: A Dmft Resultsmentioning

confidence: 99%

Parquet decomposition calculations of the electronic self-energy

et al. 2016

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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 non-perturbative numerical calculations. We show the specific example of dynamical mean field theory (DMFT) and its cluster extensions (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 [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 an RVB state, which are typical hallmarks of a pseudogap state in DCA.

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Section: A Dmft Resultsmentioning

confidence: 99%

Parquet decomposition calculations of the electronic self-energy

et al. 2016

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“…via the numerical solution of an Anderson impurity model (AIM). However a full calculation for nanostructures at the DΓA approximation level, including the solution of the parquet equations [9][10][11][12]17 , is indeed computationally expensive. In this paper we will focus on the DMFT approximation level, that can be seen as a special case of a general scheme that we call "nano-DΓA", as described in Ref.…”

Section: Introductionmentioning

confidence: 99%

Correlation effects in transport properties of interacting nanostructures

et al. 2012

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We discuss how to apply many-body methods to correlated nanoscopic systems, and provide general criteria of validity for a treatment at the dynamical mean field theory (DMFT) approximation level, in which local correlations are taken into account, while non-local ones are neglected. In this respect, we consider one of the most difficult cases for DMFT, namely for a quasi-one-dimensional molecule such as a benzene ring. The comparison against a numerically exact solution shows that non-local spatial correlations are relevant only in the limit of weak coupling between the molecule and the metallic leads and of low inter-atomic connectivity, otherwise DMFT provides a quantitative description of the system. As an application we investigate the role of correlations on electronic transport in quantum junctions, and we show that a local Mott-Hubbard crossover is a robust phenomenon in sharp nanoscopic contacts.

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“…This includes quantum Monte Carlo (QMC) methods (e.g., lattice QMC [30]), functional renormalization group [31], parquet approximation [32][33][34], and cluster extensions [35] of the dynamical mean field theory (DMFT) [36,37] such as the cellular-DMFT [38,39] or the dynamical cluster approximation (DCA) [40]. Within diagrammatic extensions [41][42][43][44][45][46][47] of DMFT, our analysis is applicable if parquet-like diagrams are included [48][49][50].…”

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“…The most obvious approach would be a direct decomposition of the full scattering amplitude F ↑↓ of Eq. (1) in all possible fluctuation channels, the so-called parquet [32][33][34]60] decomposition. This approach works well in the weakly correlated regime (small U, large doping, high T), whereas for stronger correlations it suffers from intrinsic divergences, recently discovered in the Hubbard and Falicov-Kimball models [61][62][63]; see also Ref.…”

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Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics

et al. 2015

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We demonstrate how to identify which physical processes dominate the low-energy spectral functions of correlated electron systems. We obtain an unambiguous classification through an analysis of the equation of motion for the electron self-energy in its charge, spin, and particle-particle representations. Our procedure is then employed to clarify the controversial physics responsible for the appearance of the pseudogap in correlated systems. We illustrate our method by examining the attractive and repulsive Hubbard model in two dimensions. In the latter, spin fluctuations are identified as the origin of the pseudogap, and we also explain why d-wave pairing fluctuations play a marginal role in suppressing the low-energy spectral weight, independent of their actual strength. Introduction.-Correlated electron systems display some of the most fascinating phenomena in condensed matter physics, but their understanding still represents a formidable challenge for theory and experiments. For photoemission [1] or STM [2,3] spectra, which measure single-particle quantities, information about correlation is encoded in the electronic self-energy Σ. However, due to the intrinsically many-body nature of the problems, even an exact knowledge of Σ is not sufficient for an unambiguous identification of the underlying physics. A perfect example of this is the pseudogap observed in the single-particle spectral functions of underdoped cuprates [4], and, more recently, of their nickelate analogues [5]. Although relying on different assumptions, many theoretical approaches provide self-energy results compatible with the experimental spectra. This explains the lack of a consensus about the physical origin of the pseudogap: In the case of cuprates, the pseudogap has been attributed to spin fluctuations [6-10], preformed pairs [11][12][13][14][15], Mottness [16,17], and, recently, to the interplay with charge fluctuations [18][19][20][21] or to Fermi-liquid scenarios [22]. The existence and the role of (d-wave) superconducting fluctuations [11][12][13][14][15] in the pseudogap regime are still openly debated for the basic model of correlated electrons, the Hubbard model.Experimentally, the clarification of many-body physics is augmented by a simultaneous investigation at the two-particle level, i.e., via neutron scattering [23], infrared or optical [24] and pump-probe spectroscopy [25], muon-spin relaxation [26], and correlation or coincidence two-particle spectroscopies [27][28][29]. Analogously, theoretical studies of Σ can also be supplemented by a corresponding analysis at the two-particle level. In this

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Parquet approximation for the4×4Hubbard cluster

Cited by 74 publications

References 13 publications

Parquet decomposition calculations of the electronic self-energy

Parquet decomposition calculations of the electronic self-energy

Correlation effects in transport properties of interacting nanostructures

Fluctuation Diagnostics of the Electron Self-Energy: Origin of the Pseudogap Physics

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