Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems

Area of Science:

• Condensed Matter Physics
• Quantum Mechanics
• Materials Science

Background:

• The extended Hubbard model describes interacting electrons in materials.
• Understanding magnetic properties requires accounting for nonlocal correlations and many-body effects.
• Existing methods can be computationally intensive for complex systems.

Purpose of the Study:

• To introduce a novel formalism for analyzing magnetic interactions in correlated electron systems.
• To express key magnetic properties in terms of accessible single-particle quantities.
• To provide a framework for accurate calculations in multiband systems.

Main Methods:

• Formulation of a Heisenberg-like problem using spin operators.
• Derivation of an effective exchange interaction incorporating nonlocal correlations.
• Expression of exchange interaction and spin susceptibility using single-particle properties.

Main Results:

• The derived formalism simplifies the calculation of magnetic properties.
• Results are applicable to realistic multiband systems.
• In the spin-polarized limit, the method reproduces established density functional theory expressions.

Conclusions:

• The new formalism offers a powerful tool for studying magnetic phenomena in correlated materials.
• It provides a unified description of many-body effects, particularly those dominated by bosonic fluctuations.
• The approach facilitates practical calculations for magnetic materials, bridging theory and experiment.