The meaning of orbital-free orbitals

The physical interpretation of orbitals in mean-field theories has been a subject of debate since the early days of quantum mechanics. In the context of Kohn-Sham Density Functional Theory (DFT), the derivative discontinuity is recognized as a key element linking the fundamental gap to the Kohn-Sham gap. When applying a hard bosonization approach, a mapping can be established between the Kohn-Sham system of non-interacting electrons and an orbital-free system of non-interacting bosons. This raises an important question: what is the physical meaning of the orbitals and orbital energies in the non-interacting boson system? We address this question through both theoretical analysis and computational simulations.