Effective spin-bath models for real solids and molecules

Magnetism in particular and spin physics in general are true quantum mechanical effects. Their study usually requires multi-reference methods and their effective description is often hidden in the standard description of molecules and solids in quantum chemistry. In this work we present a two step approach for the derivation of effective model descriptions of the spin physics in molecules and solids. First, we present a method that identifies the orbital basis in which a given subset of the orbitals are equivalent with the significant spin degrees of freedom in the materials. For this we introduce a metric for the spin-like character of a given linear combinations of orbitals. An optimization of this metric identifies the optimal spin-like basis orbitals. Secondly, we demonstrate a generalized Schrieffer-Wolff transformation method to derive the effective Hamiltonian acting on the subspace of the Hilbert space in which the charge degree of freedom of electrons occupying the previously identified spin-like orbitals is negligible. The application of the two steps yields an effective spin-bath Hamiltonian description of the system that allows for a targeted study of the spin physics of the material. This generalized Schrieffer-Wolff transformations is applicable to a wide range of Hamiltonians and has already been successfully employed with a selection of quantum chemistry Hamiltonians of molecules.