η -pairing states in the Hubbard model with nonuniform Hubbard interaction

The existence of η-pairing eigenstates in the fermionic Hubbard model is fundamentally rooted in the η-pairing symmetry, which may hold for systems with nonuniform Hubbard interaction U. In this work, we present a generalized Hubbard model containing a variety of pseudospin terms that break the SO₄ symmetry but retain the η-pairing symmetry. This allows us to construct a variety of correlated systems possessing η-pairing eigenstates. We exemplify our findings by considering a modified Hubbard model associated with alternative magnetic fields and on-site repulsion. We find that the same quasi-η-pairing eigenstate exhibits two distinct dynamic behaviors in the two models. Numerical results of the time evolution driven by several typical Hamiltonians accord with the analytic predictions and provide a method for the control of an η-pairing wave packet with the aid of a time-dependent Hamiltonian.