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

Abstract

The ground-state phase diagram of the S =1/2 X X Z ladder model is investigated by using the density-matrix renormalization-group method. This model is composed of two S =1/2 X X Z chains with ferromagnetic rung couplings (λ) and intra-chain anisotropy (Δ), and continuously changes from the two independent S =1/2 X X Z chains at λ=0 to the S =1 X X Z 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.