<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>η</mml:mi></mml:math>-pairing states as true scars in an extended Hubbard model
Daniel K. Mark, Olexei I. Motrunich
Abstract
The $\ensuremath{\eta}$-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [C. N. 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 $\ensuremath{\eta}$-pairing SU(2) symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [J. E. Hirsch, Physica C 158, 326 (1989)], where the $\ensuremath{\eta}$-pairing states survive without the $\ensuremath{\eta}$-pairing symmetry and become true scar states. We also discuss similarities between the $\ensuremath{\eta}$-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [M. Schecter and T. Iadecola, Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in one dimension. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several scarred models, including a spin-1/2 ${J}_{1}\ensuremath{-}{J}_{2}$ model with Dzyaloshinskii-Moriya interaction, in realistic quantum magnet settings in one and two dimensions.