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Qualitative breakdown of the noncrossing approximation for the symmetric one-channel Anderson impurity model at all temperatures

机译：对称单通道安德森杂质模型在所有温度下的非交叉近似的定性分解

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摘要

The Anderson impurity model is studied by means of the self-consistent hybridization expansions in its noncrossing (NCA) and one-crossing (OCA) approximations. We have found that for the one-channel spin-1/2 particle-hole symmetric Anderson model, the NCA results are qualitatively wrong for any temperature, even when the approximation gives the exact threshold exponents of the ionic states. Actually, the NCA solution describes an overscreened Kondo effect, because it is the same as for the two-channel infinite-U single-level Anderson model. We explicitly show that the NCA is unable to distinguish between these two very different physical systems, independently of temperature. Using the impurity entropy as an example, we show that the low-temperature values of the NCA entropy for the symmetric case yield the limit S_(imp)(T = 0) → In 2~(1/2), which corresponds to the zero temperature entropy of the overscreened Kondo model. Similar pathologies are predicted for any other thermodynamic property. On the other hand, we have found that the OCA approach lifts the artificial mapping between the models and restores correct properties of the ground state, for instance, a vanishing entropy at low enough temperatures S_(imp)(T = 0) → 0. Our results indicate that the very well known NCA should be used with caution close to the symmetric point of the Anderson model.
机译：利用非交叉（NCA）和单交叉（OCA）近似中的自洽杂交扩展研究了安德森杂质模型。我们已经发现，对于单通道自旋1/2粒子孔对称安德森模型，即使近似值给出了离子态的精确阈值指数，NCA结果在任何温度下在质上都是错误的。实际上，NCA解决方案描述了过屏的近藤效果，因为它与两通道Infinite-U单级Anderson模型相同。我们明确表明NCA无法独立于温度区分这两个非常不同的物理系统。以杂质熵为例，表明在对称情况下，NCA熵的低温值产生极限S_（imp）（T = 0）→In 2〜（1/2），对应于过筛的Kondo模型的零温度熵。对于任何其他热力学性质，也预测出类似的病理。另一方面，我们发现OCA方法提升了模型之间的人工映射并恢复了基态的正确属性，例如在足够低的温度S_（imp）（T = 0）→0时熵消失了。我们的结果表明，在安德森模型的对称点附近应谨慎使用众所周知的NCA。

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  • 来源
    《Physical review》 |2016年第8期|085139.1-085139.8|共8页
  • 作者

    C. N. Sposetti; L. O. Manuel; P. Roura-Bas;

  • 作者单位

    Instituto de Fisica Rosario (CONICET) and Universidad National de Rosario, Rosario, Argentina;

    Instituto de Fisica Rosario (CONICET) and Universidad National de Rosario, Rosario, Argentina;

    Consejo National de Investigaciones Cientificas y Tecnicas (CONICET) Argentina,Depto de Fisica CAC-CNEA, Argentina;

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