A new measure of orbital entanglement: the single-site Anderson model as an exact test case

We introduce a new measure of quantum entanglement, the orbital concurrence, designed to quantify orbital correlations in interacting multi-orbital electron systems. This quantity extends the concept of concurrence, originally developed for charge and spin degrees of freedom, to the orbital sector, providing a compact and physically transparent characterization of orbital entanglement. To test the validity and usefulness of this measure, we apply it to the single-site Anderson model, a paradigmatic and exactly solvable system that captures the essential interplay between localized correlated electrons and itinerant ones. In this framework, we derive exact, fully analytical expressions for the orbital concurrence and investigate its behavior in different regimes of interaction strength and hybridization. Our results demonstrate the diagnostic power of the proposed measure and open the way to its use in more complex multi-orbital impurities and lattice models.