Excitonic states in the one-dimensional Hubbard model

We consider the charge excitations of the half-filled Hubbard chain, which are related to electron pairs occupying the same lattice site. In the exact Bethe Ansatz eigenfunction, we separate the centre-off-mass motion by introducing the centre-off-mass and relative coordinates and wave vectors. These excitations are then interpreted as interacting quasi-particles propagating as plane waves along the chain. The two-body problem is solved for these quasi-particles. The solution suggests the existence of bound pairs, namely particle-hole excitonic states. A connection to the magnon states of the ferromagnetic Heisenberg chain is also discussed.