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Coulomb matrix elements in multi-orbital Hubbard models.

Jörg Bünemann1, Florian Gebhard2

  • 1Institut für Physik, BTU Cottbus-Senftenberg, PO Box 101344, 03013 Cottbus, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|January 13, 2017
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Summary
This summary is machine-generated.

This study identifies independent Coulomb parameters for multi-orbital Hubbard models across various point groups. These parameters simplify calculations in solid-state theory, reducing complexity for d- and f-shells.

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Area of Science:

  • Solid-state theory
  • Quantum chemistry
  • Condensed matter physics

Background:

  • Coulomb matrix elements are crucial for multi-orbital Hubbard models in solid-state theory.
  • Symmetries in these models lead to dependencies among Coulomb matrix elements.

Purpose of the Study:

  • To determine a minimal set of independent Coulomb parameters for d- and f-shells across specified point groups.
  • To express all other Coulomb matrix elements as functions of these independent parameters.
  • To analyze the spherical approximation and its first-order corrections.

Main Methods:

  • Symmetry analysis of Coulomb interactions in multi-orbital models.
  • Derivation of independent Coulomb parameters for d- and f-shells.
  • Group theory application for point groups up to 16 symmetry operations.
  • Investigation of spherical and near-spherical approximations.

Main Results:

  • A complete set of independent Coulomb parameters is determined for d- and f-shells under various point group symmetries (Oh, O, Td, Th, D6h, D4h).
  • Formulations are provided to express all Coulomb matrix elements using these independent parameters.
  • The study details the spherical approximation and its first-order corrections.

Conclusions:

  • The derived independent Coulomb parameters offer a simplified and systematic approach to electronic structure calculations using multi-orbital Hubbard models.
  • This work provides a valuable tool for researchers in solid-state theory, enabling more efficient and accurate modeling of correlated electron systems.
  • The findings facilitate a deeper understanding of electron interactions in materials with complex symmetries.