Transport through quantum dots: A combined DMRG and cluster-embedding study

TL;DR

This paper analyzes finite-size effects in numerical methods for quantum dot transport, improving the reliability of embedded-cluster approximation (ECA) results by identifying optimal clusters and comparing with DMRG.

Contribution

It provides a detailed finite-size analysis for quantum dot systems, resolving controversies and proposing a practical method to select optimal clusters for ECA using DMRG as a benchmark.

Findings

Finite-size effects depend on odd-even cluster properties.

Optimal clusters for observing the Kondo effect have total spin zero.

ECA reliability range is extended with the proposed cluster selection method.

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.