Eta-pairing states as true scars in an extended Hubbard Model

The eta-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called "eta-pairing SU(2)" symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [Physica C 158, 326 (1989)], where the eta-pairing states survive without the eta-pairing symmetry and become true scar states. We also discuss similarities between the eta-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in 1D. We also generalize these terms to arbitrary bipartite lattices.