Exact Solutions And Quantum Phase Transitions In The One-Dimensional Bose-Hubbard Model

Strongly correlated systems are of importance in view of their relevance to the theory ofhigh-Tc superconductivety. Hard-core Bose-Hubbard model is one of such basic models. The modeldescribes hard-core bosons hopping on a destrete lattice, which is exactly solvable.In this thesis, the quantum phase transitions in the one-dimensional hard-core Bose-Hubbard modelis studied, in which only the nearest neighbor hopping is considered. Quantum phase transitional be-haviors of the ground state energy, the ground state entanglement, and particle number occupancy asfunctions of control parameter are analyzed. The thesis consists of four chapters. The background ofstrongly correlated systems and a few key quantities are provided in Chapter 1. Some important physicalquantities and algorithm will be shown in Chapter 2. The quantum phase transitional behaviors of theground state energy, the ground state entanglement and particle number occupancy as function of controlparameter will be studied in Chapter 3. A short summary will be shown in Chapter 4.