Can exact (local) Kohn-Sham potential reproduce band gaps?: Analysis using an analytically solvable two- and three-body models

We have clarified whether the exact (local) Kohn-Sham(KS) potential reproduces the exact band gap or not [1]. We have investigated the analytically solvable interacting two- and three-body models and calculated the exact electron levels through the one-particle Green's function of the two-body system analytically. Subsequently, we constructed the exact KS potential analytically and compared the obtained KS levels with exact ones. Then, we have found that KS-DFT even with the exact (local) KS potential does not reproduce the exact band gaps.

[1] J. Phys.: Condens. Matter 30, 435604 (2018).