Three-body problem in a multiband Hubbard model

We consider the three-body problem in a generic multiband lattice, and analyze the dispersion of the trimer states that are made of two spin-up arrow fermions and a spin-down arrow fermion due to an on-site attraction in between. Based on a variational approach, we first obtain the exact solution in the form of a set of coupled integral equations, and then reduce it to an eigenvalue problem. As an illustration we apply our theory to the sawtooth lattice, and numerically show that energetically stable trimers are allowed in a two-band setting, which is in sharp contrast with the single-band linear-chain model. In particular, we also reveal that the trimers have a nearly flat dispersion when formed in a flat band, which is unlike the highly dispersive spectrum of its dimers.