The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on odd-even effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.
Chiral Mott insulators in frustrated Bose-Hubbard models on ladders and two-dimensional lattices: a combined perturbative and density matrix renormalization group study
Multiple impurities and combined local density approximations in Site-Occupation Embedding Theory
占位嵌入理论（SOET）是密度泛函理论在理论上对模型哈密顿量的精确多行列式推广。SOET最近发展的各种扩展[Senjean等人，Phys. Rev. B 97，235105（2018）]在这项工作中进行了探索。向前迈出的重要一步是将理论推广到多个杂质位置。我们还提出了一种新的单杂质密度泛函近似（DFA），它将二能级（2L）Hubbard系统的密度泛函杂质相关能与Bethe局域密度近似（BALDA）结合起来，计算（无限）哈伯德模型的全相关能.为了检验新的分布函数，用密度矩阵重整化群方法（DMRG）自洽地计算了杂质相互作用的波函数。双占领和每个网站的能量表达式已被推导和实施的一维情况下。的结果进行了详细的分析，特别关注的错误引起的能量泛函单独或自洽收敛密度。在所有的DFA（包括以前提出的），组合2L-BALDA是一个在所有的相关性和密度制度，表现最好的。最后，扩展在新的方向，如分区DFT型重新制定SOET，基于投影的SOET方法，或SOET与格林函数的组合，简要讨论了作为一个角度。
