Kikuchi et al. Reply: In the preceding Comment [1], Gu and Su (GS) reported the finite temperature transfer matrix renormalization group (TMRG) method results for the distorted diamond chain (DDC) model. They pointed out that the double-peak behavior of T found in experiment cannot be reproduced by our parameter set J 1 :J 2 :J 3 1:1:25:0:45 [2], but well fitted by J 1 :J 2 :J 3z 1:1:9: ÿ 0:3 with J 3x =J 3z J 3y =J 3z 1:7.In response to GS's Comment, we have performed the additional density matrix renormalization group (DMRG) and the exact diagonalization calculations for the magnetization curve MH at T 0 of the DDC model with GS's parameter set. As can be seen from Fig. 1, the DMRG MH curve with GS's parameter set does not well explain the experimental results.The positional relations between Cu 2 ions corresponding to J 1 and J 3 are very similar to each other as can be seen in the schematic view of the crystal structure of Cu 3 CO 3 2 OH 2 in Fig. (1b) of our previous Letter [2]. The distance of two Cu 2 ions corresponding to J 1 is 327.5 pm with bond angle 113.7 and that to J 3 is 329.0 pm with bond angle 113.5 . Thus it is unlikely that J 1 is antiferromagnetic without the XXZ anisotropy while J 3 is ferromagnetic with strong XXZ anisotropy. Further, as far as we know, such a strong XXZ anisotropy has not been observed at all in the S 1=2 spin systems of Cu 2 ions.The double-peak behaviors of T and CT are not necessarily attributed to the frustration effect. The mechanism for the double-peak behaviors will be as follows. In the case of J 2 J 1 , jJ 3 j as lowering the temperature, spins coupled by J 2 are going to form singlet dimers at first. The remaining spins are nearly free because they are separated PRL 97,

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We determine the magnetic phase diagram of the S = 1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.KEYWORDS: frustration, cusp, 1/3 plateau, even-odd effect For the purpose of clarifying the role of the frustration in low-dimensional quantum spin systems, the S = 1/2 antiferromagnetic zigzag spin chain has been attracting considerable attention, since it minimally contains the frustrating interaction without loss of the translational invariance.1-4) The Hamiltonian of the model is given bywhere S is the S = 1/2 spin operator, H is the magnetic field, and J 1 and J 2 denote the nearest and next nearest neighbor couplings, respectively. We introduce the notation α = J 2 /J 1 for simplicity. Recently, the zigzag chain was realized as SrCuO 2 , 5) Cu(ampy)Br 2 , 6)(N 2 H 5 )CuCl 3 7) and F 2 PIMNH. 8)The Hamiltonian (1) has a very simple form, but captures a variety of behaviors induced by the frustration. In particular, the zigzag chain in a magnetic field has been studied actively [9][10][11][12][13] and it has been clarified that cusp singularities appear near the saturation field and/or in the low field region for α ≤ 0.6, in accordance with the frustration-driven shape change of the dispersion curve of the elementary excitations.12-14) However, the magnetic phase diagram including the strongly frustrated region (α > 0.6) has not been acquired yet. Here we remark that the magnetization curve of α = 0.6 is still quite different from the one in the α → ∞ limit (see Fig.2 (a)). Thus, as α is increased beyond α = 0.6, the intrinsic structural change of the magnetization curve can be expected particularly around α ≃ 1, where the most significant competition is achieved.In this paper we address the magnetization process of the zigzag chain in the strongly frustrated region(α > 0.6), using the density matrix renormalization group (DMRG) method.15) We then find that the obtained phase diagram exhibits rich physics, as is shown in Fig.1. For 0.56 < ∼ α < ∼ 1.25, the magnetization plateau appears at 1/3 of the full moment, accompanying the spontaneous breaking of the translational symmetry with the period three. Moreover, the cusp singularities in the magnetization curve show quite interesting behavior; as α is increased, the high field cusp merges into the 1/3 plateau at α ≃ 0.82. Also the low field cusp merges the 1/3 plateau at α ≃ 0.7, but it appears again when α > 0.7. In addition, we find an interesting even-odd effect in the magnetization curve for α > 0.7. In analyzing the phase diagram, an important feature of the zigzag chain is that the Hamiltonian (1) interpolates between the single Heisenberg chain(J 2 = 0) and the double Hei...