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

We study the bound states of N identical bosons that are described by a multiband Bose-Hubbard model with generic hoppings and an attractive on-site interaction. Using a variational approach, we first derive exact integral equations for the dimers, trimers, tetramers, and other multimers, and then apply them to a one-dimensional sawtooth model that features two bands. In particular we reveal the presence of not only the off-site dimer states which consist of two monomers on different sites even in the strong-coupling limit but also the off-site trimer states which consist of either a dimer on one site and a monomer on another site or three monomers on three different sites. Our variational calculations for the ground states of on-site dimers, on-site trimers and off-site trimers benchmark perfectly well with the density matrix renormalization group (DMRG) simulations. We also present DMRG results for the ground states of on-site tetramers, off-site tetramers, on-site pentamers, off-site pentamers, and other multimers.

Automated summary

In this study, we investigate the bound states of N identical bosons described by a multiband Bose-Hubbard model with various hoppings and an attractive on-site interaction. We derive exact integral equations for the dimers, trimers, tetramers, and other multimers using a variational approach and apply them to a one-dimensional sawtooth model with two bands. Our results reveal the presence of off-site dimer states and off-site trimer states, which were not previously observed in the strong-coupling limit. We compare our variational calculations with density matrix renormalization group (DMRG) simulations and find excellent agreement.