Erratum: “Ground-State Phase Diagram of Frustrated Antiferromagnetic S = 1 Chain with Uniaxial Single-Ion-Type Anisotropy” [J. Phys. Soc. Jpn. 71, 319 (2002)

Abstract

In the paper, it was incorrectly mentioned that by the exactdiagonalization calculation for small systems, the ground state of the model (1.4) was found to belong to the subspace of Stotal 1⁄4 0 with even parity.1) Although it is the case for the periodic chains and for a wide parameter region of the open chains, we have noticed that the ground state with odd parity appears in some parameter points of the open chains, as shown in Fig. 1 of this erratum. We note that this is a boundary effect in small systems with frustration, and the infinite-system density-matrix renormalization-group (DMRG) calculation in the original paper, which was performed for the subspace of Stotal 1⁄4 0 with even parity, should capture the ground-state properties in the thermodynamic limit correctly. Indeed, we have newly performed the infinite-system DMRG for the whole subspace of Stotal 1⁄4 0 including both even and odd parity states, and obtained the same results as the previous ones within a numerical accuracy. Therefore, our conclusions remain the same. We also correct misprints, which do not affect our conclusions. (i) In Figs. 2(a), 4(a), and 6(a), the distance r of the chiral correlation C ðrÞ was shifted by one due to a simple error in the data processing. The label for the x-axis should read r þ 1 instead of r. (ii) In Figs. 2(b), 3, 4(b), and 5(a), the sign of the string correlation was reversed erroneously: The minus sign should be removed. (iii) In Fig. 4, the number of kept states m for d 1⁄4 1:10 was not 350 but 300. We have checked that the results with these m’s are almost identical. In Fig. 6(a), in addition to j 1⁄4 0:800, the data for j 1⁄4 0:810 were obtained with m 1⁄4 500. Accordingly, in Fig. 1, a cross, which indicates the point of high-precision calculation, should be added at ðj; dÞ 1⁄4 ð0:810; 0:30Þ.