自洽图解方法中的不稳定性及其修复方法
Instabilities in self-consistent diagrammatic approaches and how to cure them
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- Institute of Solid State Physics, TU Wien（维也纳工业大学固体物理研究所）
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中文总结 AI 辅助
本文发现自洽图解方法在强关联区域收敛到非物理固定点的根源在于迭代稳定性，而非方法本身失效，并提出通过反转雅可比不稳定本征方向来稳定物理固定点的通用修复方案。
中文摘要 AI 辅助
虽然自洽图解方法被广泛用于计算关联量子材料的物理性质，但恰恰在观察到最令人兴奋的物理现象的参数区域内，其适用性可能受到严重阻碍。其中一个主要问题被称为“误导性收敛”，即迭代方案倾向于收敛到中间至强电子相互作用下的非物理固定点，而无论计算的数值精度如何。在此，我们明确验证了在玻色子交换形式的一般图解框架中定义的几种成熟的自洽多电子方法中，该问题的根源完全在于各自迭代方案的稳定性条件，而非其自洽图解描述的内在失效。这一见解提供了一种简单而通用的补救措施，正如最近在《物理评论快报》137, 016502 (2026) 中所提出的：通过反转与自洽算法固定点相关的雅可比矩阵的不稳定本征方向，重新定义迭代过程。我们通过对测试平台（可精确求解的模型）进行系统计算，展示了该过程的成功结果。我们的结果表明，我们所考虑的图解方案的物理固定点实际上可以在整个参数范围内实现稳定，包括最具挑战性的非微扰/强耦合区域。
英文摘要
While self-consistent diagrammatic approaches are widely used to compute the physical properties of correlated quantum materials, their applicability may get severely hindered precisely in the parameter regions, where the most exciting physics is observed. One of the major issues, referred to as "misleading convergence", is the tendency of iterative schemes to converge to unphysical fixed points for intermediate-to-strong electronic interactions, regardless of numerical accuracy of the computation. Here, we explicitly verify that the origin of this problem in several established self-consistent many-electron approaches, defined in the general diagrammatic framework of the boson-exchange formalism, resides exclusively in the stability condition of the respective iteration schemes, and not in an intrinsic breakdown of their self-consistent diagrammatic description. This insight enables a simple and general remedy, as recently proposed in Phys. Rev. Lett. 137, 016502 (2026): The redefinition of the iterative procedure, by inverting the unstable eigendirections of the Jacobian associated to the fixed point of the self-consistent algorithm. We illustrate the successful outcome of this procedure by means of systematic calculations performed on testbed, exactly solvable, models. Our results demonstrate that the physical fixed point of the diagrammatic schemes we considered can be stabilized, de facto, across the entire parameter range, including the most challenging nonperturbative/strong-coupling regimes.
