Eur. Phys. J. B 67, 527-542 (2009)
https://doi.org/10.1140/epjb/e2009-00036-4

Transport through quantum dots: a combined DMRG and embedded-cluster approximation study

¹ Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, 37831 Tennessee, USA
² Department of Physics and Astronomy, University of Tennessee, Knoxville, 37996 Tennessee, USA
³ Department of Physics, Oakland University, Rochester, 48309 Michigan, USA
⁴ Department of Physics and Astronomy, Ohio University, Athens, 45701 Ohio, USA
⁵ National High Magnetic Field Laboratory and Department of Physics, Florida State University, Tallahassee, 32306 FL, USA
⁶ Theoretical Division T-11, Los Alamos National Laboratory, Los Alamos, 87545 NM, USA
⁷ Microsoft Project Q, University of California, Santa Barbara, 93106 CA, USA
⁸ Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, 20742 MD, USA
⁹ Departmento de Física J.J. Giambiagi, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
¹⁰ Departamento de Física Aplicada, Universidad de Alicante, San Vicente del Raspeig, 03690 Alicante, Spain
¹¹ Departamento de Física, Pontificia Universidade Católica do Rio de Janeiro, 38071 Rio de Janeiro, Brazil

Corresponding author: ^a fabian.heidrich-meisner@physik.rwth-aachen.de

Received: 7 June 2008
Revised: 5 November 2008
Published online: 10 February 2009

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.