Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

Kaufmann, Josef; Gunacker, Patrik; Held, Karsten

doi:10.1103/physrevb.96.035114

Cited by 37 publications

(34 citation statements)

References 54 publications

(90 reference statements)

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“…87,102,103) Essentially this eliminates finite-size effects of the frequency box, and further improves the numerical results of the local vertex function.…”

Section: Ct-qmc Calculation Of the Local Vertexmentioning

confidence: 95%

“…Additionally, one can define a particle-hole-transverse and a particle-particle frequency notation as, e. g., in Refs., 103,104) but in this case we use the convention described in. 87) We have also introduced the bare two-particle propagator…”

Section: Hamiltonian and Formalismmentioning

confidence: 99%

“…A more thorough derivation of the above equations is provided elsewhere. 87) In Fig. 3 we show the improvement introduced by the vertex asymptotics by comparing a slice of F for the benchmark material SrVO 3 in the density and magnetic channel, each with and without vertex asymptotics.…”

Section: Vertex Asymptoticsmentioning

confidence: 99%

“…3 with the value of the full vertex on the y-axis; the last column shows two cuts for zero bosonic frequency, ω 0 . The shaded areas indicate where, based on considerations for the atomic limit, 87) the asymptotic instead of the full QMC vertex is used in the AbinitioDΓA. This figure demonstrates that in the shaded region the asymptotic tail well represents the data without any noticeable off-set but with considerably less noise.…”

Section: Vertex Asymptoticsmentioning

confidence: 99%

“…In Section 2, we introduce the multi-orbital Hamiltonian that we want to solve and our notation regarding Green's functions and vertices. Section 3 is devoted to the continuoustime quantum Monte Carlo calculation (CT-QMC) of the local two-particle vertex, using vertex asymptotics 87) and worm sampling. 88) In Section 4, we recapitulate the AbinitioDΓA algorithm 86,89) which starts with the local vertex plus the bare non-local interaction, constructs through the Bethe-Salpeter equation the non-local full vertex and through the SchwingerDyson equation the non-local self-energy.…”

Section: Introductionmentioning

confidence: 99%

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Towards ab initio Calculations with the Dynamical Vertex Approximation

et al. 2018

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While key effects of the many-body problem-such as Kondo and Mott physics-can be understood in terms of onsite correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioDΓA). Finally, we highlight the potential of AbinitioDΓA by detailing results for the prototypical correlated metal SrVO 3 .

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“…87,102,103) Essentially this eliminates finite-size effects of the frequency box, and further improves the numerical results of the local vertex function.…”

Section: Ct-qmc Calculation Of the Local Vertexmentioning

confidence: 95%

Section: Hamiltonian and Formalismmentioning

confidence: 99%

Section: Vertex Asymptoticsmentioning

confidence: 99%

Section: Vertex Asymptoticsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards ab initio Calculations with the Dynamical Vertex Approximation

et al. 2018

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w2dynamics: Local one- and two-particle quantities from dynamical mean field theory

Wallerberger

Hausoel

Gunacker

et al. 2019

Computer Physics Communications

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We describe the hybridization-expansion continuous-time quantum Monte Carlo code package "w2dynamics", developed in Wien and Würzburg. We discuss the main features of this multi-orbital quantum impurity solver for the Anderson impurity model, dynamical mean field theory as well as its coupling to density functional theory. The w2dynamics package allows for calculating one-and two-particle quantities; it includes worm and further novel sampling schemes. Details about its download, installation, functioning and the relevant parameters are provided.

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The AbinitioDΓA Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory

Galler

Thunström

Kaufmann

et al. 2019

Computer Physics Communications

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The ab initio extension of the dynamical vertex approximation (DΓA) method allows for realistic materials calculations that include non-local correlations beyond GW and dynamical mean-field theory. Here, we discuss the AbinitioDΓA algorithm, its implementation and usage in detail, and make the program package available to the scientific community.Keywords: Strongly correlated electron systems; dynamical mean-field theory; dynamical vertex approximation; electronic structure calculations PROGRAM SUMMARYProgram Title: AbinitioDΓA Licensing provisions: GNU General Public License (GPLv3) Operating system: Linux, Unix, macOS Programming language: Fortran95 and Python Required dependencies: MPI, LAPACK, BLAS, HDF5 (≥ 1.8.12), Python (≥ 2.7), h5py (≥ 2.5.0), numpy (≥ 1.9.1) Optional dependencies: pip, matplotlib (≥ 1.5.1), scipy (≥ 0.14.0) Supplementary material: Test case files and step-by-step instructions Nature of problem: Realistic materials calculations including non-local correlations beyond dynamical mean-field theory (DMFT) as well as non-local interactions. Solving the Bethe-Salpeter equation for multiple orbitals. Determining momentum-resolved susceptibilities in DMFT.Solution method: Ab initio dynamical vertex approximation: starting from the local two-particle vertex and constructing from it the local DMFT correlations, the GW diagrams, and further non-local correlations, e.g., spin fluctuations. Efficient solution of the Bethe-Salpeter equation, avoiding divergencies in the irreducible vertex in the particle-hole channel by reformulating the problem in terms of the full vertex. Parallelization with respect to the bosonic frequency and transferred momentum.Additional comments including Restrictions and Unusual features: As input, a Hamiltonian derived, e.g., from density functional theory and a DMFT solution thereof is needed including a local twoparticle vertex calculated at DMFT self-consistency. Hitherto the AbinitioDΓA program package is restricted to SU(2) symmetric problems. A so-called λ correction or self-consistency is not yet implemented in the AbinitioDΓA code. Susceptibilities are so far only calculated within DMFT, not the dynamical vertex approximation.

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Continuous-time quantum Monte Carlo calculation of multiorbital vertex asymptotics

Cited by 37 publications

References 54 publications

Towards ab initio Calculations with the Dynamical Vertex Approximation

Towards ab initio Calculations with the Dynamical Vertex Approximation

w2dynamics: Local one- and two-particle quantities from dynamical mean field theory

The AbinitioDΓA Project v1.0: Non-local correlations beyond and susceptibilities within dynamical mean-field theory

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