Corner states of the breezing Pyrochlore lattice are protected by the Z4 symmetry as a typical example of the bulk-edge/boundary correspondence using Z4 Berry phase. With on-site Coulomb interaction, these zero-dimensional localized states exhibit charge-spin separation. The charge is gapped and the spin is gapless. The model in 3D has been studied by the negative sign-free fermion Monte Carlo technique. The negative U case is also mentioned in relation to the Shiba transformation. Have a look at our recent paper, “Higher-order topological Mott insulator on the pyrochlore lattice” by Yuichi Otsuka, Tsuneya Yoshida, Koji Kudo, Seiji Yunoki & Yasuhiro Hatsugai, Scientific Reports volume 11, Article number: 20270 (2021) published on Oct.12 (2021)