Numerical Study on the Ground-State Phase Diagram of the S = 1/2 XXZ Ladder Model

The ground-state phase diagram of the S = 1/2 XXZ ladder model is investigated by using the density-matrix renormalization-group method. This model is composed of two S = 1/2 XXZ chains with ferromagnetic rung couplings (λ) and intra-chain anisotropy (Δ), and continuously changes from the two independent S = 1/2 XXZ chains at λ = 0 to the S = 1 XXZ chain in the limit of λ → ∞. It is shown that there exist edge states at Δ = 1 and λ = 1 in relation to the four-fold degeneracy of the ground state and that an excitation gap opens nearly at λ = 0 for 0.8 ⩽Δ ⩽ 1. In addition, it is clarified that the transition between the Haldane phase and the antiferromagnetic phase occurs at λ= 1.15 ± 0.01 for Δ = 1. A possible phase diagram in the λ-Δ plane is proposed, which is consistent with the scaling analysis based on the bosonization method.