Symmetry-based approach to ground-state properties of the one-dimensional negative-U Bose–Hubbard trimer model

It is shown that the ground state of the one-dimensional negative-U three-site Bose–Hubbard (trimer) model with periodic (boundary) condition or for a closed chain can be solved almost exactly within a small symmetric subspace with a few boson-trines through an analysis of the percentage of the boson-trines in the ground state. It is also shown that there is a sudden increase of the boson-trine content of the ground state near the critical point of the quantum phase transition, which may be used as an effective order parameter to study the phase transition of the model. The ground-state energy per particle and the entanglement measure with the variation of the control parameter are also analyzed to show their transitional behavior. (paper)