Ground State Properties Of The Three-Site Extended Bose-Hubbard Model

In this thesis,the extended Bose-Hubbard(BH)model with number-dependent multi-site and infinite-range hopping is proposed,which,similar to the original BH model,describes a phase transition between the delocalized superfluid(SF)phase and localized Mott insulator(MI)phase.It is shown that the extended model with the local Euclidean E2 symmetry is exactly solvable when on-site local potentials are included,while the model without local potentials is quasi-exactly solvable,which means only a part of the excited states including the ground state being exactly solvable.As applications of the exact solutions,the ground state of the model with three sites with the filling factor ? > 1 is analyzed.Energy spectrum of the model with different number of particles is analyzed.The ground state probabilities to detect n particle on a single site P_n,and its relation with the multi-partite entanglement are studied.It is shown that the model-independent entanglement measure is relate with P_n,which,therefore,is practically useful and can be regarded as an important order parameter because P_nis measurable experimentally.Finally,some other ground state properties of the model are also analyzed,which show quantum phase transitional behaviors of the model with the variation of the control parameter.