Generalized η-pairing States in Extended SU(N) Hubbard Models

η-pairing states are exact eigenstates of the SU(2) Hubbard model that exhibit two-particle off-diagonal long-range order (ODLRO) [1]. Although these states are not ground states, there has been a recent surge of interest in such states in the context of superconductivity and superfluidity, and quantum many-body scars. Recently, the SU(N) generalization of the Hubbard model has attracted much attention since it was realized with ultracold atoms in optical lattices [2].  Despite its obvious importance, the counterpart of η-pairing states in the SU(N) (N > 2) Hubbard model was missing.

 Here we present N-particle generalizations of η-pairing states in a chain of SU(N) fermions and show that they are exact eigenstates of extended SU(N) Hubbard models [3]. When N is even, these states exhibit N-particle ODLRO. On the other hand, when N is odd, the correlation decays exponentially toward the other end of the chain but shows a revival at the other end. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.

[1] C. N. Yang, Phys. Rev. Lett. 63, 2144 (1989).

[2] S. Taie, R. Yamazaki, S. Sugawa, and Y. Takahashi, Nat. Phys. 8, 825 (2012). 

[3] H. Yoshida and H. Katsura, arXiv:2109.07010 (2021).