Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory

Otsuki, Junya; Yoshimi, Kazuyoshi; Shinaoka, Hiroshi; Nomura, Yusuke

doi:10.1103/physrevb.99.165134

Cited by 20 publications

(17 citation statements)

References 41 publications

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“…This question can be decided by considering the strong coupling limit, which shows that only Π (2) in equation (19) correctly describes the effective exchange: It is shown in Appendix F that for very large coupling U t, T the static DMFT spin susceptibility of the halffilled Hubbard model takes the form, see also Ref. [35],…”

Section: A Trilex-like Approximationmentioning

confidence: 99%

“…In the second line χ sp 0 = 2/(π sp,−1 0 −U sp ) was used. Defining the effective exchange as I q = −π sp,−2 0Π sp (q 0 ) one arrives at the strong coupling form of the DMFT spin susceptibility [35]. For very large interaction the local moment is fully developed and χ sp,−1 0 ≈ −T , leading to equation (21) in the main text.…”

Section: Dmftmentioning

confidence: 99%

“…Both expressions contain the nonlocal bubbleX 0 ν (q) = k G k G k+q − g ν g ν+ω , which can be simplified in the strong coupling limit using similar steps as in Ref. [35]. For small hybridization ∆ ≈ 0 one can expand Green's function G k ≈ g ν + g ν ε k g ν , hence, X 0 ν (q) ≈ k g ν g 2 ν+ω ε k+q + g 2 ν g ν+ω ε k + g 2 ν g 2 ν+ω ε k ε k+q…”

Section: Trilex-like Approximationmentioning

confidence: 99%

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Efficient evaluation of the polarization function in dynamical mean-field theory

Krien

2019

Phys. Rev. B

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The dynamical susceptibility of strongly correlated electronic systems can be calculated within the framework of the dynamical mean-field theory (DMFT). The required measurement of the four-point vertex of the auxiliary impurity model is however costly and restricted to a finite grid of Matsubara frequencies, leading to a cutoff error. It is shown that the propagation of this error to the lattice response function can be minimized by virtue of an exact decomposition of the DMFT polarization function into local and nonlocal parts. The former is measured directly by the impurity solver, while the latter is given in terms of a ladder equation for the Hedin vertex that features an unprecedentedly fast decay of frequency summations compared to previous calculation schemes, such as the one of the dual boson approach. At strong coupling the local approximation of the TRILEX approach is viable, but vertex corrections to the polarization should be dropped on equal footing to recover the correct prefactor of the effective exchange. In finite dimensions the DMFT susceptibility exhibits spurious mean-field criticality, therefore, a two-particle self-consistent and frequency-dependent correction term is introduced, similar to the Moriya-λ correction of the dynamical vertex approximation. Applications to the two-and three-dimensional Hubbard models on the square and cubic lattices show that the expected critical behavior near an antiferromagnetic instability is recovered. arXiv:1901.02832v2 [cond-mat.str-el]

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Section: A Trilex-like Approximationmentioning

confidence: 99%

Section: Dmftmentioning

confidence: 99%

Section: Trilex-like Approximationmentioning

confidence: 99%

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Efficient evaluation of the polarization function in dynamical mean-field theory

Krien

2019

Phys. Rev. B

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“…When the single-orbital Hubbard model is a good description, the magnetic interactions in the Mott insulating region can be obtained by strong-coupling perturbation expansion. The strong-coupling expansion becomes valid in the region U W with the bandwidth W (in the square lattice W = 8t) [60]. RbCa 2 NiO 3 and A 2 NiO 2 Br 2 (A = Ba 0.5 La 0.5 ) with U/t = 9.522 and 10.637, respectively [18], satisfy the condition U > W .…”

Section: A Strong-coupling Expansionmentioning

confidence: 99%

Magnetic exchange coupling in cuprate-analog d9 nickelates

Nomura

Nomoto

Hirayama

et al. 2020

Phys. Rev. Research

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Motivated by the recent discovery of superconductivity in doped NdNiO 2 , we study the magnetic exchange interaction J in layered d 9 nickelates from first principles. The mother compounds of the high-T c cuprates belong to the charge-transfer regime in the Zaanen-Sawatzky-Allen diagram and have J larger than 100 meV. While this feature makes the cuprates very different from other transition metal oxides, it is of great interest whether layered d 9 nickelates can also have such a large J. However, one complexity is that NdNiO 2 is not a Mott insulator due to carrier doping from the block layer. To compare the cuprates and d 9 nickelates on an equal basis, we study RbCa 2 NiO 3 and A 2 NiO 2 Br 2 (A denotes a cation with a valence of 2.5+), which were recently designed theoretically by block-layer engineering. These nickelates are free from the self-doping effect and belong to the Mott-Hubbard regime. We show that these nickelates share a common thread with the high-T c cuprates in that they also have a significant exchange interaction J as large as about 100 meV.

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“…Corrections from higher frequencies outside the box are treated using the procedure described in Appendix B of Ref. [32]. The corresponding physical quantities are obtained by summation over the fermionic frequencies.…”

Section: Dmft Calculations For Single-band Hubbard Model On a Square mentioning

confidence: 99%

Overcomplete compact representation of two-particle Green's functions

et al. 2018

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Many-body calculations at the two-particle level require a compact representation of two-particle Green's functions. In this paper, we introduce a sparse sampling scheme in the Matsubara frequency domain as well as a tensor network representation for two-particle Green's functions. The sparse sampling is based on the intermediate representation basis and allows an accurate extraction of the generalized susceptibility from a reduced set of Matsubara frequencies. The tensor network representation provides a system independent way to compress the information carried by two-particle Green's functions. We demonstrate efficiency of the present scheme for calculations of static and dynamic susceptibilities in single-and two-band Hubbard models in the framework of dynamical mean-field theory.

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Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-field theory

Cited by 20 publications

References 41 publications

Efficient evaluation of the polarization function in dynamical mean-field theory

Efficient evaluation of the polarization function in dynamical mean-field theory

Magnetic exchange coupling in cuprate-analog d9 nickelates

Overcomplete compact representation of two-particle Green's functions

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