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

TL;DR

This paper investigates bound states of bosons in a multiband Bose-Hubbard model, deriving exact equations and analyzing various multimers, with results validated by DMRG simulations.

Contribution

It introduces a variational approach to derive integral equations for multimers in a multiband Bose-Hubbard model and provides comprehensive DMRG validation.

Findings

Identification of offsite dimer and trimer states in a two-band model

Exact integral equations for multimers derived and validated

Numerical results for various multimers including tetramers and pentamers

Abstract

We study the bound states of $N$ identical bosons that are described by a multiband Bose-Hubbard model with generic hoppings and an attractive onsite 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 offsite dimer states which consist of two monomers on different sites even in the strong-coupling limit but also the offsite 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 onsite dimers, onsite trimers and offsite trimers benchmark perfectly well with the DMRG simulations. We also present DMRG results for the ground states of onsite tetramers, offsite tetramers, onsite pentamers, offsite pentamers, and for those of other multimers.