Quantum Phase Transtions In One-Dimensional Strongly Correlated Systems

In this thesis we use density-matrix renormalization group methods to investi-gate the quantum phase transitions in two kinds of one-dimensional strong correlated systems. One is a half-filled one-dimensional superlattice Hubbard model with an al-ternating orbital energy c/2 and on-site Coulomb repulsion UA and UB. The other is a spinless fermion model with the nearest and next-nearest-neighbor repulsions. We cal-culate the spin and charge correlation functions, static structure factors and the energy gap. With the help of finite-size scaling analysis, We establish the ground-state phase diagram of both models at zero temperature.In the half-filled one-dimensional superlattice Hubbard model, we observe an in-commensurate charge correlation phase around the particle-hole symmetric point(ε= (UA-UB)/2) for UA >> UB.In the incommensurate region, the location of the peak in the static charge structure factor shifts away from q=π。For a given UA, the incom-mensurate region appears only if UB is lower than a critical value UB. With decreasing UA, the critical UBc decreases. With the investigation of the nearest-neigbour and next nearest-neigbour charge correlation, we find for UA >> UB, the charge fluctuation on-site B is much larger than that of the on-site A. With the increase of UA, the B-B charge correlation is enhanced and the A-B and A-A correlations are suppressed. This competition between the NN and NNN correlations results in a shift of the peak of N(q). For UB=O, we find a transition from the BI phase to the correlated metallic phase at the criticalεc=UA/2. Atε= UA/2, both the charge and spin excitations are gapless while the charge and spin correlation exhibit the asymptotic behavior of the power-law decay as in the Tomonaga-Luttinger liquid. For UB> 0, we find two-step phase tran-sitions with increasingε: the BI phase forε<εc1, the BOI phase forεc1<ε<εc2 and the MI phase forε>εc2. This process is the same as that in the ionic Hubbard model. By analyzing the asymptotic behavior of the correlation functions, we find that the correlation becomes stronger as the gap is reduced, in particular, the correlation is strongest when the gap vanishes.In the one-dimensional V1-V2 spinless fermion model, we find that the BO corre-lation function B(r) and its static structure factor NB(q) can be employed to accurately determine the BO phase boundaries. Near the 2kF-CDW-BO boundary, B(r) is pos- itive and NB(q) peaks at q=0. NB(q=0) has its maximum at the 2kF-CDW-BO transition point. Around the BO-metal critical point, B(r) is staggered and the max-imum of NB(q=π) gives the transition point. At two boundaries of the BO phase, B(r) decays most slowly as a power law. In the 2kF-CDW phase and BO phase, B(r) decays exponentially. The first derivative of the charge structure factor Nc(q=π) and the second derivative of the energy are expect to diverge at the 2kF-CDW-BO transition point, which indicates that a second-order transition occurs. The boundary between the metallic and 4kF-CDW phases is determined by the decay behavior of the charge correlation C(r)∝1/r.