Role of three-particle vertex within dual fermion calculations

Ribic, T.; Gunacker, Patrik; Iskakov, Sergei; Wallerberger, Markus; Rohringer, G.; Rubtsov, A. N.; Gull, Emanuel; Held, Karsten

doi:10.1103/physrevb.96.235127

Cited by 30 publications

(22 citation statements)

References 34 publications

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“…This procedure does not allow us to calculate all components of the multiorbital vertex function, a limitation that was overcome by Gunacker et al, 2015 using worm sampling. Let us also note a first calculation of the local threeparticle vertex using CT-INT (Hafermann et al, 2009c), CT-AUX, and CT-HYB (Ribic et al, 2017a). Slices through this three-particle vertex show similar structures as the two-particle vertex shown above.…”

Section: Exact Diagonalizationmentioning

confidence: 72%

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

et al. 2018

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Strong electronic correlations pose one of the biggest challenges to solid state theory. Recently developed methods that address this problem by starting with the local, eminently important correlations of dynamical mean field theory (DMFT) are reviewed. In addition, nonlocal correlations on all length scales are generated through Feynman diagrams, with a local two-particle vertex instead of the bare Coulomb interaction as a building block. With these diagrammatic extensions of DMFT long-range charge-, magnetic-, and superconducting fluctuations as well as (quantum) criticality can be addressed in strongly correlated electron systems. An overview is provided of the successes and results achieved mainly for model Hamiltonians and an outline is given of future prospects for realistic material calculations. PACS numbers: 71.10.-w,71.10.Fd,71.27.+a CONTENTS 42 5. One and zero dimensions 43 B. Heavy fermions and Kondo lattice model (KLM) 44 C. Falicov-Kimball (FK) model 45 D. Models of Disorder 47 E. Non-local interactions and multiorbitals 48 V. Open source implementations 51 VI. Conclusion and outlook 51 References 53 arXiv:1705.00024v2 [cond-mat.str-el]

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Section: Exact Diagonalizationmentioning

confidence: 72%

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

et al. 2018

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“…DMFT calculations are performed with the continuous time auxiliary field quantum Monte Carlo method [43,44] with submatrix updates [45]. DF is accurate at high temperature [46] but uncontrolled in practice in the sense that adding systematic corrections, while possible in theory [47,48], is not feasible for the parameters studied here. A detailed assessment of the approximation errors of the susceptibility and the single-particle properties on the square lattice [49] showed that while dopingand interaction dependent scaling effects were present, the overall momentum dependence was accurate.…”

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confidence: 99%

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Gull

2020

Phys. Rev. Research

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We study magnetic and charge susceptibilities in the half-filled two-dimensional triangular Hubbard model within the dual fermion approximation in the metallic, Mott insulating, and crossover regions of parameter space. In the insulating state, we find strong spin fluctuations at the K point at low energy corresponding to the 120 • antiferromagnetic order. These spin fluctuations persist into the metallic phase and move to higher energy. We also present data for simulated neutron spectroscopy and spin-lattice relaxation times, and perform direct comparisons to inelastic neutron spectroscopy experiments on the triangular material Ba8CoNb6O24 and to the relaxation times on κ-(ET)2Cu2(CN)3. Finally, we present charge susceptibilities in different areas of parameter space, which should correspond to momentum-resolved electron-loss spectroscopy measurements on triangular compounds., suggests that these compounds are close to a two-dimensional triangular structure and exhibit interesting electron correlation behavior including, potentially, a quantum spin liquid phase [7] in the ground state [8]. These compounds, as well as the low energy physics of the fully isotropic triangular material Ba 8 CoNb 6 O 24 [9], may be described by a half-filled single orbital Hubbard model on a triangular two-dimensional lattice, with an on-site Coulomb interaction strength comparable to or larger than the bandwidth [10].Because of the subtle competition of metallic, ordered, and spin liquid phases in the ground state, this model has been studied extensively with a wide range of numerical tools, including exact diagonalization (ED) [11][12][13], density matrix renormalization group theory (DMRG) [8], variational Monte Carlo (VMC) [14][15][16][17], variational cluster approximation [18][19][20], strong coupling expansions [21], path integral renormalization group techniques [22], and cluster dynamical mean field theory (DMFT) in the cellular [23][24][25][26][27] and dynamical cluster [28,29] variants. The focus in most of these studies has been on the precise location of the phase boundaries, ordering (or the absence thereof), and on the nature of these phases.Experimentally, much of our knowledge about correlated triangular systems is obtained from single-and two-particle scattering experiments such as photoemission [30], Raman spectroscopy [31], nuclear magnetic resonance (NMR) [2,32], or inelastic neutron scattering [9,33]. To understand these experimental results, it is necessary to calculate the corresponding response functions as a function of energy and momentum. For neutron spectroscopy and angular-resolved photoemission spectroscopy, in particular, both fine momentum and energy resolutions are desired. Such results are difficult to obtain, as computational methods formulated on finite lattices (such as ED, DMRG, and cluster DMFT) pro-

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“…Hence, we calculate at least selected threeparticle diagrams as an error estimate after convergence of the two-particle approach, in the same way as in Ref. 28.…”

Section: Recapitulation Of the Methodsmentioning

confidence: 99%

Impact of self-consistency in dual fermion calculations

2018

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The dual fermion (DF) method allows for calculating corrections due to non-local correlations relative to an effective impurity model. Choosing the impurity as that of a dynamical mean field theory (DMFT) solution at self-consistency is popular, and the corrections from dual fermion theory are physically meaningful. We investigate the effect of choosing the impurity instead in a selfconsistent manner and find for the two dimensional Hubbard model an exponentially increase of the correlation length and susceptibility at low temperatures. There are pronounced differences for the two self-consistency schemes that are discussed in the literature; the self-consistent DF solution can even be more metallic than the DMFT solution.arXiv:1805.10996v1 [cond-mat.str-el]

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Role of three-particle vertex within dual fermion calculations

Cited by 30 publications

References 34 publications

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory

Magnetic and charge susceptibilities in the half-filled triangular lattice Hubbard model

Impact of self-consistency in dual fermion calculations

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