Coulomb matrix elements in multi-orbital Hubbard models

Abstract

Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a $d$-shell and a $f$-shell and all point groups with up to $16$ elements ($O_h$, $O$, $T_d$, $T_h$, $D_{6h}$, and $D_{4h}$). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

25 pages + 44 pages supplementary material (in the source files)

References in corpus (4)

• Multi-band Gutzwiller wave functions for general on-site interactions
• The Fermi surface of Sr2RuO4: spin-orbit and anisotropic Coulomb interaction effects
• Cubic interaction parameters for t2g Wannier orbitals
• Gutzwiller Density Functional Theory: a formal derivation and application to ferromagnetic nickel

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• The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries