Ground State Phase Diagram of the One Dimensional S=1/2 XXZ Model with Dimerization and Quadrumerization

The one dimensional S=1/2 XXZ model with dimerization (1-j) and quadrumerization \delta is studied by the numerical exact diagonalization of finite size systems. Using the conformal field theory and the level spectroscopy method, we calculate the ground state phase diagram with XY-like anisotropy \Delta (0<\Delta<1). The ground states of this model contain the Haldane state, S=1 dimer state, S=1 large-D state and S=1/2 dimer state as limiting cases. The \Delta and \delta-dependence of the critical exponent \nu of the energy gap is determined from the conformal dimensions of excited states.