  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. Our study of the spin-1
XY model also leads us to several new scarred models, including a spin-1/2
$J_1-J_2$ model with Dzyaloshinkskii-Moriya interaction, in realistic quantum
magnet settings in 1D and 2D.
