arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2003.03871cond-mat.mes-hall
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用选择组态相互作用和微扰理论精确有效地描述量子纳米结构中相互作用载流子

Accurate and efficient description of interacting carriers in quantum nanostructures by selected configuration interaction and perturbation theory

Moritz Cygorek, Matthew Otten, Marek Korkusinski, Pawel Hawrylak

摘要:

基于原子紧束缚计算,结合组态的迭代选择和微扰理论,提出了一种计算百万原子量子纳米结构中相互作用载流子多体态的方法.这种方法使大型激子复合物和多电子系统的调查与近全组态相互作用的准确性,即使只有一个小子空间的完整的多体希尔伯特空间进行采样,从而节省数量级的计算资源。这种方法的重要优点是,收敛是由一个单一的参数,阈值控制,并且基态和激发态可以同等对待。我们证明了该方法的极端效率,由多达13个激子组成的复合物的数值研究,这需要填充状态的第四个电子壳层。我们发现,该方法一般收敛速度快的阈值的函数,从一个显着的增强由于微扰校正受益。单粒子基态的选择的作用进行了讨论。结果表明,该算法收敛速度更快的Hartree-Fock基础上只有高电荷系统,其中库仑排斥占主导地位。最后,基于二阶微扰能量修正只依赖于多体哈密顿量的非对角元素的观察,我们提出了一种只需要相对少量的库仑矩阵元素就可以精确计算多体态的方法。

英文摘要:

We present a method to calculate many-body states of interacting carriers in million atom quantum nanostructures based on atomistic tight-binding calculations and a combination of iterative selection of configurations and perturbation theory. This method enables investigations of large excitonic complexes and multi-electron systems with near full configuration interaction accuracy, even though only a small subspace of the full many-body Hilbert space is sampled, thus saving orders of magnitudes in computational resources. Important advantages of this method are that the convergence is controlled by a single parameter, the threshold, and that ground and excited states can be treated on an equal footing. We demonstrate the extreme efficiency of the method by numerical studies of complexes composed of up to 13 excitons, which requires filling of states up to the fourth electronic shell. We find that the method generally converges fast as a function of the threshold, profiting from a significant enhancement due to the perturbative corrections. The role of the choice of single-particle basis states is discussed. It is found that the algorithm converges faster in the Hartree-Fock basis only for highly charged systems, where Coulomb repulsion dominates. Finally, based on the observation that second order perturbative energy corrections only depend on off-diagonal elements of the many-body Hamiltonian, we present a way to accurately calculate many-body states that requires only a relatively small number of Coulomb matrix elements.

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