A many-body approach to crystal field theory

TL;DR

This paper introduces a self-consistent many-body method to compute crystal field parameters ab initio, integrating Green function theory and traditional crystal field approaches for better accuracy in strongly-interacting systems.

Contribution

It develops a novel first-principles framework combining many-body theory with crystal field calculations, enabling more accurate modeling of strongly-interacting electron systems.

Findings

Provides a unified formalism encompassing Green functions and crystal field theory.

Enables ab initio calculation of crystal field parameters.

Expected to improve results for strongly-interacting electrons.

Abstract

A self-consistent many-body approach is proposed to build a first-principles crystal field theory, where crystal field parameters are calculated ab initio. Many-body theory is used to write the energy of the interacting system as a function of the density matrix of the noninteracting system. A variation of the energy with respect to the density matrix gives an effective Hamiltonian that is diagonalized to determine the density matrix providing the lowest energy. The equations are written in terms of the Hopf algebra of functional derivatives with respect to external fermionic sources. This approach contains the many-body theory of Green functions as a special case, and the usual crystal field theory as a first approximation. Therefore, it is expected to provide good results for strongly-interacting electron systems.