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

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