Fermionic bound states on a one-dimensional lattice

We study bound states of two fermions with opposite spins in an extended Hubbard chain. The particles interact when located both on a site or on adjacent sites. We find three different types of bound states. Type U is predominantly formed of basis states with both fermions on the same site, while two states of type V originate from both fermions occupying neighboring sites. Type U and one of the states from type V are symmetric with respect to spin flips. The remaining one from type V is antisymmetric. V states disappear by merging with the two-particle continuum below some critical wave number. All bound states become compact for wave numbers at the edge of the Brillouin zone.