Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions

TL;DR

This paper presents a new method using broken-symmetry mean-field solutions, specifically Hartree-Fock wave functions, to more comprehensively determine coupling constants in spin clusters, including multi-center interactions.

Contribution

The work introduces a novel approach that extracts a wider range of coupling parameters from BS solutions by considering Hamiltonian and overlap elements, surpassing traditional energy-only methods.

Findings

Enables construction of comprehensive spin Hamiltonians including multi-center terms.

Demonstrates the method on small Hubbard model clusters, matching exact results.

Provides deeper insight into spin interactions beyond conventional Heisenberg models.

Abstract

Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory (DFT). The energies of these configurations are interpreted in terms of the Heisenberg model to determine coupling constants for spin pairs. However, this energy-based procedure has inherent limitations, primarily in its inability to provide information on isotropic spin interactions beyond those included in the Heisenberg model. Biquadratic exchange or multi-center terms, for example, are usually inaccessible and hence assumed to be negligible. The present work introduces a novel approach employing BS mean-field solutions, specifically Hartree-Fock wave functions, for the construction of effective spin Hamiltonians. This expanded method facilitates the extraction of a broader range of coupling parameters by considering not only the energies, but also Hamiltonian and overlap elements between different BS states. We demonstrate how comprehensive s = 1/2 Hamiltonians, including multi-center terms, can be straightforwardly constructed from a complete set of BS solutions. The approach is exemplified for small clusters within the context of the half-filled single-band Hubbard model. This allows to contrast the current strategy against exact results, thereby offering an enriched understanding of the spin-Hamiltonian construction from BS solutions.