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

Abstract

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.

Computing local multipoint correlators using the numerical renormalization group

“…As before, γ 0 > 0 should be taken infinitesimal or small but finite. Equations ( 5), (9), and (10) give the spectral representation for KF p correlators, concluding our summary of the results derived in Ref. 1.…”

“…Such functions are needed, e.g., in diagrammatic extensions [2] of dynamical mean field theory (DMFT) [3,4]. There, one starts from the self-consistent DMFT solution of an impurity model, capturing local correlations, and aims to include nonlocal correlations by utilizing various diagrammatic relations, taking local 4p functions as input [2,[5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

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

“…This serves as an input for subsequent calculations of physical susceptibility and for diagrammatic extensions of DMFT 44 that use the local vertex as a building block. The package directly interfaces with post-DMFT packages such as AbinitioDGA 71 and LadderDGA. 72 2.…”

Zoology of spin and orbital fluctuations in ultrathin oxide films

“…The DMFT self-consistency cycle as well as the sam-pling of the two-particle Green's function is done by continuous-time quantum Monte Carlo simulations in the hybridization expansion 32,33 using w2dynamics 34 with worm sampling 35 . Momentum-dependent DMFT susceptibilities are calculated from the local vertex, using the AbinitioDΓA 36,37 program package.…”