利用动量空间中的随机变分方法将光激发半导体中的多体问题转化为少体问题
Turning many-body problems to few-body ones in photoexcited semiconductors using the stochastic variational method in momentum space, SVM-k
摘要：
我们发展了一种有效的计算技术，通过随机变分方法（SVM）计算光激发半导体中的复合激子态。电子气和激子态之间的多体相互作用通过导带中的费米空穴体现在这个问题中，当电子被拉出费米海以结合光激发的电子-空穴对时引入。我们考虑了复合物中可分辨粒子之间的直接库仑相互作用、交换诱导的带隙重整化效应以及电子与其导带空穴之间的电子-空穴交换相互作用。我们提供了潜在的矩阵元素的解析表达式，使用一种技术，使我们能够规避的困难所施加的低能量的电子状态的占领在导带。我们讨论的计算步骤，应该实施，以执行计算，以及如何提取单个粒子的动能的复杂，平均粒子间的距离，和密度分布。
英文摘要：
We develop an efficient computational technique to calculate composite excitonic states in photoexcited semiconductors through the stochastic variational method (SVM). Many-body interactions between an electron gas and the excitonic state are embodied in the problem through Fermi holes in the conduction band, introduced when electrons are pulled out of the Fermi sea to bind the photoexcited electron-hole pair. We consider the direct Coulomb interaction between distinguishable particles in the complex, the exchange-induced band-gap renormalization effect, and electron-hole exchange interaction between an electron and its conduction-band hole. We provide analytical expressions for potential matrix elements, using a technique that allows us to circumvent the difficulty imposed by the occupation of low-energy electron states in the conduction band. We discuss the computational steps one should implement in order to perform the calculation, and how to extract kinetic energies of individual particles in the complex, average inter-particle distances, and density distributions.
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