Subspace representations in ab initio methods for strongly correlated systems

TL;DR

This paper introduces a tensorially consistent subspace occupancy formalism for ab initio methods like DFT+U and DFT+DMFT, ensuring local, Hermitian, and invariant properties in strongly correlated systems.

Contribution

It provides a generalized, tensorially consistent definition of subspace occupancy matrices suitable for nonorthogonal projectors in strongly correlated ab initio methods.

Findings

Occupancy matrices are tensorial and local to the correlated subspace.

Potential and forces are Hermitian without symmetrization.

Formalism demonstrated in a DFT+U study with self-consistent projectors.

Abstract

We present a generalized definition of subspace occupancy matrices in ab initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT, which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT+U in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies and ionic forces is preserved. We illustrate the effect of this formalism in a DFT+U study using self-consistently determined projectors.