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

Abstract

The one dimensional S=1/2 XXZ model with dimerization (1-j) and quadrumerization δis 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 Δ(0<Δ<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 Δand δ-dependence of the critical exponent νof the energy gap is determined from the conformal dimensions of excited states.