Automatic generation of Hamiltonians describing spins in a bath from a wide range of interacting systems

We describe an automated algebraic Schrieffer-Wolff approach that yields a description of complex systems, in which the interactions between spin-like orbitals and designated bath-orbitals no longer involve any particle transfer, such that a representation of the spin-like orbitals by means of simple spin degrees of freedom becomes feasible.

To this end we introduce a metric by which one can quantify the spin-character of orbitals in complex systems, meaning the extent to which an orbital is strictly singly occupied in the system's low-energy Hilbert space.

Using said metric, a sequence of basis rotations can be constructed that yields the specific set of basis orbitals for which the spin-character is maximized.

This then allows for the separation of a system's orbitals into spin-like orbitals and bath-orbitals, between which the hybridization coupling is suppressed.