An effective action for Bose-Hubbard model with two- and three-body on-site interaction in a square optical lattice is derived in the frame of a strong-coupling approach developed by Sengupta and Dupuis. From this effective action, superfluid-Mott insulator (MI) phase transition, excitation spectrum and momentum distribution for two phases are calculated by taking into account Gaussian fluctuation about the saddle-point approximation. In addition the effects of three-body interaction are also discussed.
Abstract It is shown that the extended one-dimensional dimer Bose–Hubbard model with multi-body interactions can be solved exactly by using the algebraic Bethe ansatz mainly due to the site-permutation S 2 symmetry. The solution for the model with up to three-particle hopping and three-body on-site interaction is explicitly shown. As an example of the application, lower part of the excitation energy levels and the ground-state entanglement measure of the standard Bose–Hubbard Hamiltonian with the attractive two-body on-site interaction plus the three-body on-site interaction for 100 bosons with variation of the control parameter are calculated by using the exact solution. It is shown that the attractive three-body on-site interaction reinforces the critical point entanglement of the system, which may be helpful for design of an optical lattice for ultracold atoms or a tuneable superconducting quantum interference device with maximal entanglement.
Repulsively interacting particles in a periodic potential can form bound composite objects with long lifetimes, as has been observed experimentally [Winkler et al., Nature (London) 441, 853 (2006)]. In this paper, a complete two-particle solution of one-dimensional periodical potential was derived in a strong interaction regime, where the on-site approximation of a two-body interaction in the Bose-Hubbard model (BHM) is extended to include the interaction of nearest neighbors, which results in atom-pair hopping. The energy spectrum of the bound pair is drastically reshaped due to the pair-hopping term, and complex eigenenergy corresponding to metastable states is also found that has not been discovered in the usual BHM. When the absolute value of a center-of-mass quasimomentum wave vector is greater than a critical value (
∣K∣>Kc), two bound-pair solutions are found. Furthermore, the spatial and momentum distributions of the bound pair displays a crossover from dark to bright soliton-like solutions in the extended BHM. Our results reduce to that of the usual BHM in the weak interaction case.