Abstract
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.
