One-dimensional Optical Lattices Based On Dmrg Algorithm Quantum Phase Transition Of Chinese Super Cold Atomic Gas

Ever since Bose-Einstein condensation realized in experiment for the first time in1995, the field of ultracold atoms have progressed at an astonishing rate, especially the system of ultracold atomic gases in optical lattice, which has being a hot research topic in physics.Although there have been some analytical and numerical researches about this phenomena, many algorithms have some limitations. So in this paper, two basic models of the ultracold atoms in one dimension optical lattice, Bose-Hubbard model and Extended Bose-Hubbard model are studied by Density Matrix Renormalization Group, which is the most accurate and effective numerical method to calculate strongly correlated systems of low dimension. Then the local density, chemical potential and the compressibility are obtained which can characterize the feature of different phase. At the same time the critical conditions can be calculated.For the one dimensional Bose-Hubbard model, when the hopping energy J is much larger than the potential energy U, the system is in the superfluid state, which is gapless and compressible. However, when U is much lager than J, the Mott insulor state, which is gaped and incompressible, is found at integer densities and the superfluid state is found at noninteger densities. From the phase diagram obtained by calculation, the critical condition of the transition from Mott insulator to superfluid are obtained.While for the one dimensional Extended Bose-Hubbard model, a different state Charge Density Wave which is gaped and incompressible appears, because of the introduction of additional nearest-neighbor interaction V. In this phase, the bosons occupy alternate sites. For small values of J, the Charge Density Wave state is found at half-integer densities. While at the integer densities, depending on the value of V either a Mott insultor or a Charge Density Wave state appears. In addition a superfluid ground state appears when the density is neither interger nor half-interger. Similarly, the CDW-SF transition critical conditions is calculated.