Erratum: “Ground State Phase Diagram of Frustrated S = 1 XXZ Chains: Chiral Ordered Phases” [J. Phys. Soc. Jpn. 69, 259 (2000)

Abstract

In the paper, it was incorrectly mentioned that the exactdiagonalization calculation for small systems found that the ground state of the model (1.1) belonged to the subspace of S total 1⁄4 0 with even parity.1) (We call this subspace PE below.) While it is the case for the periodic chains2) and for a wide parameter region of the open chains, we have noticed that the ground state with odd parity appears in some narrow parameter regions 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 for the subspace PE performed in the original paper should capture the groundstate properties in the thermodynamic limit correctly. Indeed, we have newly performed the infinite-system DMRG for the whole subspace of S total 1⁄4 0 including both even and odd parity states (we call this subspace PEO), and obtained essentially the same results as the previous ones for the subspace PE. For example, as for the estimates of jc1 and jc2 shown in Table II, those for 1⁄4 0, 0.2, and 0.4 remain the same, while comparing the results for PE and PEO, we modify the errors of the estimates for 1⁄4 0:6 (0.8) from ðjc1; jc2Þ 1⁄4 ð0:642 0:002; 0:660 0:003Þ [ð0:715 0:003; 0:720 0:002Þ] to ð0:642þ0:004 0:002; 0:660þ0:009 0:003Þ [ð0:715þ0:005 0:003; 0:720þ0:009 0:002Þ]. The other results in the paper, including the phase diagram and the estimates of critical exponents, remain the same within a numerical accuracy. Therefore, our conclusions remain valid. We also correct misprints and typographical errors, which do not affect our conclusions. (i) In Figs. 2(b) and 5, 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 + 1 instead of r. (ii) Equation (3.2) should read