Comment on “Bounding and approximating parabolas for the spectrum of Heisenberg spin systems” by H.-J. Schmidt, J. Schnack and M. Luban
Comment on “Bounding and approximating parabolas for the spectrum of Heisenberg spin systems” by H.-J. Schmidt, J. Schnack and M. Luban
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对 H.-J Schmidt、J. Schnack 和 M. Luban 的“海森堡自旋系统谱的边界和近似抛物线”的评论
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发表时间：
2002
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影响因子：
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通讯作者：
O. Waldmann
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作者：
O. Waldmann
最近，施密特等人。证明了海森堡自旋系统的能谱是由两条抛物线约束的，即依赖于S(S+1)的总自旋量子数的直线。证明对满足弱齐性条件的同核HSS成立。此外，数值研究的各种HSS的精确谱的极值位于近似抛物线上，称为转动带，这可以通过移动边界抛物线来获得。有鉴于此，有人认为能谱的转动能带结构(RBS)是HSS的普遍行为。此外，由于对于所讨论的例子，近似抛物线非常接近于谱的真实边界，因此有人声称该方法允许预测一般HSS的谱的详细形状和相关性质。在这篇评论中，我将通过实例说明RBS假说不适用于一般的HSS。特别是，弱齐性既不是HSS表现出与RBS相同谱的充要条件，也不是充分条件。
Recently, Schmidt et al. proved that the energy spectrum of a Heisenberg spin system (HSS) is bounded by two parabolas, i.e. lines which depend on the total spin quantum number S as S(S+1). The prove holds for homonuclear HSSs which fulfill a weak homogenity condition. Moreover, the extremal values of the exact spectrum of various HSS which were studied numerically were found to lie on approximate parabolas, named rotational bands, which could be obtained by a shift of the boundary parabolas. In view of this, it has been claimed that the rotational band structure (RBS) of the energy spectrum is a general behavior of HSSs. Furthermore, since the approximate parabolas are very close to the true boundaries of the spectrum for the examples discussed, it has been claimed that the methods allow to predict the detailed shape of the spectrum and related properties for a general HSS. In this comment I will show by means of examples that the RBS hypothesis is not valid for general HSSs. In particular, weak homogenity is neither a necessary nor a sufficient condition for a HSS to exhibit a spectrum with RBS.