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We study the bound states of $N$ identical bosons that are described by amultiband Bose-Hubbard model with generic hoppings and an attractive onsiteinteraction. Using a variational approach, we first derive exact integralequations for the dimers, trimers, tetramers, and other multimers, and thenapply them to a one-dimensional sawtooth model that features two bands. Inparticular we reveal the presence of not only the offsite dimer states whichconsist of two monomers on different sites even in the strong-coupling limitbut also the offsite trimer states which consist of either a dimer on one siteand a monomer on another site or three monomers on three different sites. Ourvariational calculations for the ground states of onsite dimers, onsite trimersand offsite trimers benchmark perfectly well with the DMRG simulations. We alsopresent DMRG results for the ground states of onsite tetramers, offsitetetramers, onsite pentamers, offsite pentamers, and for those of othermultimers.

Dimers, trimers, tetramers, and other multimers in a multiband Bose-Hubbard model