Two-Particle-Self-Consistent Approach for the Hubbard Model

Tremblay, A.-M. S.

doi:10.1007/978-3-642-21831-6_13

Cited by 22 publications

(30 citation statements)

References 154 publications

(288 reference statements)

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“…It is worth noticing that the proposed scheme follows, to some extent, the ideas of the TPSC approach for the Hubbard model 31,97 . There, RPA ladders have been constructed with different values U d and U m in the charge and spin channels, respectively.…”

Section: Towards An Improved Version Of Ladder Dγamentioning

confidence: 99%

Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

2016

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In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band-edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation (DΓA), to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps, through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth, but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchangedriven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.

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Section: Towards An Improved Version Of Ladder Dγamentioning

confidence: 99%

Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

2016

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“…This is called the Slater transition 8 . Kyung et al 9 have argued for this scenario based on the two-particle self-consistent approach [10][11][12] (TPSC).…”

Section: Introductionmentioning

confidence: 99%

Precursors of the insulating state in the square-lattice Hubbard model

Loon¹,

Hafermann

Katsnelson³

2018

Phys. Rev. B

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We study the two-dimensional square lattice Hubbard model for small to moderate interaction strengths 1 ≤ U/t ≤ 4 by means of the ladder dual fermion approach. The non-local correlations beyond dynamical mean-field theory lower the potential energy, lead to a maximum in the uniform susceptibility and induce a pseudogap in the density of states. While the self-energy exhibits precursors of a possible insulating phase linked to the appearance of long-range fluctuations, the metallic phase persists within the accessible temperature range. Finite-size effects affect results qualitatively. Upper bounds on the crossover temperature are found to be significantly lower than previously reported dynamical vertex approximation results at U/t = 1.

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“…In this section, we use the non-perturbative Two-Particle Self-Consistent (TPSC) approach 33,34 . This approach respects the Pauli principle, the Mermin-Wagner theorem and conversation laws.…”

Section: Finite Temperature Results and Tpscmentioning

confidence: 99%

“…The formal derivation is given in Refs. 34,53. Here, we simply present the equations that are solved.…”

Section: A Tpscmentioning

confidence: 99%

“…Nevertheless, it can be accurate away from the critical point and provide leading order estimates for the exponents. The TwoParticle-Self-Consistent (TPSC) theory 33,34 is a related approach that has critical behavior similar to that of Moriya, including logarithmic corrections 35 . It has the advantage that although it is an approximate solution to the Hubbard model, it is quantitatively very close to benchmark Quantum Monte Carlo results 33 .…”

Section: Introductionmentioning

confidence: 99%

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Breakdown of Fermi liquid behavior at the(π,π)=2kFspin-density wave quantum-critical point: The case of electron-doped cuprates

et al. 2012

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Many correlated materials display a quantum critical point between a paramagnetic and a spindensity wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here we consider the case where pairs of hot spots coalesce, and the wave vector (π, π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility and the self-energy at the hot spots are found using the Two-Particle-SelfConsistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudo-nesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξ scales like 1/T , namely z = 1 instead of the naive z = 2, the (π, π) static spin susceptibility χ like 1/ √ T , and the imaginary part of the self-energy at the hot spots like T 3/2 . The correction T −1 1 ∼ T 3/2 to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as −ω 3/2 log ω. This is less singular than earlier predictions of the form −ω log ω. The difference arises from the effects of umklapp terms that were not included in previous studies.

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Two-Particle-Self-Consistent Approach for the Hubbard Model

Cited by 22 publications

References 154 publications

Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

Impact of nonlocal correlations over different energy scales: A dynamical vertex approximation study

Precursors of the insulating state in the square-lattice Hubbard model

Breakdown of Fermi liquid behavior at the(π,π)=2kFspin-density wave quantum-critical point: The case of electron-doped cuprates

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