电子-声子问题的累积量方法。I.微扰展开
Cumulant methods for electron-phonon problems. I. Perturbative expansions
摘要：
在这项工作中，我们研究的能力的累积展开（CE）捕获单粒子光谱信息的电子-声子耦合系统在零温度和有限的温度。特别是，我们提出了一个全面的研究的第二和第四阶CE的一维Holstein模型相比，数值精确的方法。我们调查两个有限大小的系统以及热力学极限的方法，绘制系统的行为之间的区别和联系，并远离热力学极限，使CE的能力，以捕捉整个范围内的波矢量的实时频率信息的更好的理解。我们发现，零电子动量，光谱函数很好地描述了在低温和高温下的二阶CE。然而，对于非零电子动量，CE仅在高温下是准确的。我们分析了四阶累积量，发现虽然它改善了对单粒子格林函数中编码的短时动力学的描述，但它可以在时域中引入发散以及谱函数中的非物理负谱权。当表现良好时，四阶CE确实对二阶CE提供了显著的精确校正。最后，我们使用我们的结果来评论使用CE作为一种工具，用于计算传输行为的现实从头算材料建模。
英文摘要：
In this work we investigate the ability of the cumulant expansion (CE) to capture one-particle spectral information in electron-phonon coupled systems at both zero and finite temperatures. In particular, we present a comprehensive study of the second- and fourth-order CE for the one-dimensional Holstein model as compared with numerically exact methods. We investigate both finite sized systems as well as the approach to the thermodynamic limit, drawing distinctions and connections between the behavior of systems in and away from the thermodynamic limit that enable a greater understanding of the ability of the CE to capture real-frequency information across the full range of wave vectors. We find that for zero electronic momentum, the spectral function is well described by the second-order CE at low and high temperatures. However, for non-zero electronic momenta, the CE is only accurate at high temperature. We analyze the fourth-order cumulant, and find that while it improves the description of the short-time dynamics encoded in the one-particle Green's function, it can introduce divergences in the time domain as well as unphysical negative spectral weight in the spectral function. When well-behaved, the fourth-order CE does provide notable accurate corrections to the second-order CE. Finally, we use our results to comment on the use of the CE as a tool for calculating transport behavior in the realistic ab initio modeling of materials.
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