# Effective Heisenberg model and exchange interaction for strongly correlated systems

## TL;DR

This paper develops an effective Heisenberg model from the extended Hubbard model, incorporating nonlocal correlations, and expresses exchange interactions in terms of single-particle quantities for realistic multiband system calculations.

## Contribution

It introduces a formalism linking the extended Hubbard model to a Heisenberg-like problem, accounting for nonlocal correlations and simplifying calculations of magnetic properties.

## Key findings

- Exchange interaction expressed via single-particle quantities
- Formalism reduces to DFT expressions in the spin-polarized limit
- Applicable to realistic multiband systems

## Abstract

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and magnetic susceptibility are expressed in terms of single-particle quantities, which can be obtained efficiently in realistic calculations of multiband systems. In the strongly spin-polarized limit, when the local magnetic moment is well-defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.