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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.
To describe the interaction of molecular vibrations with electrons at a quantum dot contacted to metallic leads, we extend an analytical approach that we previously developed for the many-polaron problem. Our scheme is based on an incomplete variatio
We employ the functional renormalization group to study the effects of phonon-assisted tunneling on the nonequilibrium steady-state transport through a single level molecular quantum dot coupled to electronic leads. Within the framework of the spinle
The transmission of electrons through a non-interacting tight-binding chain with an interacting side quantum dot (QD) is analized. When the Kondo effect develops at the dot the conductance presents a wide minimum, reaching zero at the unitary limit.
We consider transport through a vibrating molecular quantum dot contacted to macroscopic leads acting as charge reservoirs. In the equilibrium and nonequilibrium regime, we study the formation of a polaron-like transient state at the quantum dot for
We introduce a real time version of the functional renormalization group which allows to study correlation effects on nonequilibrium transport through quantum dots. Our method is equally capable to address (i) the relaxation out of a nonequilibrium i