Manifestation of the Upper Hubbard band in the 2D Hubbard model at low electron density

We consider the 2D Hubbard model in the strong-coupling case (U>>W) and at low electron density (nd^2<<1). We find an antibound state as a pole in the two-particle T-matrix. The contribution of this pole in the self-energy reproduces a two-pole structure in the dressed one-particle Green-function similar to the Hubbard-I approximation. We also discuss briefly the Engelbrecht-Randeria mode which corresponds to the pairing of two holes below the bottom of the band for U>>W and low electron density. Both poles produce non-trivial corrections to Landau Fermi-liquid picture already at low electron density but do not destroy it in 2D