论文标题
电子 - 光子问题的累积方法。 ii。自一致的累积扩展
Cumulant methods for electron-phonon problems. II. The self-consistent cumulant expansion
论文作者
论文摘要
在这项工作中，我们提出了自洽的累积膨胀（SC-CE），并研究了其具有和不带声子分散的一维荷斯坦模型的准确性。我们表明，对于有限的晶格大小，SC-CE方程的数值集成在长期内变得不稳定。当在热力学极限中研究系统时，该缺陷得到了部分改善，从而证明了SC-CE纠正了（非分散性）荷斯坦模型中标准扰动CE的许多缺陷。在更现实的荷斯坦模型中产生的天然声子阻尼使SC-CE稳定，从而可以对该方法进行完整的评估。在这里，我们发现自矛盾会彻底纠正扰动CE中发现的许多故障，但也引入了一些非物理特征。最后，我们评论SC-CE作为计算Green在通用多体问题中的功能的工具的潜在用途。
In this work we present a self-consistent cumulant expansion (SC-CE) and investigate its accuracy for the one-dimensional Holstein model with and without phonon dispersion. We show that for finite lattices sizes, the numerical integration of the SC-CE equations becomes unstable at long times. This defect is partially ameliorated when studying systems in the thermodynamic limit, enabling the demonstration that the SC-CE corrects many deficits of the standard perturbative CE in the (non-dispersive) Holstein model. The natural phonon damping that arises in the more realistic dispersed Holstein model renders the SC-CE stable, allowing for a complete assessment of the method. Here we find that self-consistency dramatically corrects many of the failures found in the perturbative CE, but also introduces some unphysical features. Finally, we comment on the potential use of SC-CE as a tool for calculating Green's functions in generic many-body problems.
