Transport through quantum dots: A combined DMRG and embedded-cluster approximation study
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 s...
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todo:paper_14346028_v67_n4_p527_HeidrichMeisner2023-10-03T16:14:33Z Transport through quantum dots: A combined DMRG and embedded-cluster approximation study Heidrich-Meisner, F. Martins, G.B. Büsser, C.A. Al-Hassanieh, K.A. Feiguin, A.E. Chiappe, G. Anda, E.V. Dagotto, E. Cluster approximations Exact diagonalization Exact methods Finite sizes Finite systems Finite-size analysis Finite-size effects Ground-state densities Numerical results Numerical solutions Parameter ranges Practical procedures Quantum dots Time-dependent density matrixes Electric resistance Kondo effect Magnetic materials Numerical methods Optical waveguides Quantum chemistry Quantum theory Statistical mechanics Semiconductor quantum dots 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. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_14346028_v67_n4_p527_HeidrichMeisner |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Cluster approximations Exact diagonalization Exact methods Finite sizes Finite systems Finite-size analysis Finite-size effects Ground-state densities Numerical results Numerical solutions Parameter ranges Practical procedures Quantum dots Time-dependent density matrixes Electric resistance Kondo effect Magnetic materials Numerical methods Optical waveguides Quantum chemistry Quantum theory Statistical mechanics Semiconductor quantum dots |
| spellingShingle |
Cluster approximations Exact diagonalization Exact methods Finite sizes Finite systems Finite-size analysis Finite-size effects Ground-state densities Numerical results Numerical solutions Parameter ranges Practical procedures Quantum dots Time-dependent density matrixes Electric resistance Kondo effect Magnetic materials Numerical methods Optical waveguides Quantum chemistry Quantum theory Statistical mechanics Semiconductor quantum dots Heidrich-Meisner, F. Martins, G.B. Büsser, C.A. Al-Hassanieh, K.A. Feiguin, A.E. Chiappe, G. Anda, E.V. Dagotto, E. Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| topic_facet |
Cluster approximations Exact diagonalization Exact methods Finite sizes Finite systems Finite-size analysis Finite-size effects Ground-state densities Numerical results Numerical solutions Parameter ranges Practical procedures Quantum dots Time-dependent density matrixes Electric resistance Kondo effect Magnetic materials Numerical methods Optical waveguides Quantum chemistry Quantum theory Statistical mechanics Semiconductor quantum dots |
| description |
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. © 2009 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg. |
| format |
JOUR |
| author |
Heidrich-Meisner, F. Martins, G.B. Büsser, C.A. Al-Hassanieh, K.A. Feiguin, A.E. Chiappe, G. Anda, E.V. Dagotto, E. |
| author_facet |
Heidrich-Meisner, F. Martins, G.B. Büsser, C.A. Al-Hassanieh, K.A. Feiguin, A.E. Chiappe, G. Anda, E.V. Dagotto, E. |
| author_sort |
Heidrich-Meisner, F. |
| title |
Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| title_short |
Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| title_full |
Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| title_fullStr |
Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| title_full_unstemmed |
Transport through quantum dots: A combined DMRG and embedded-cluster approximation study |
| title_sort |
transport through quantum dots: a combined dmrg and embedded-cluster approximation study |
| url |
http://hdl.handle.net/20.500.12110/paper_14346028_v67_n4_p527_HeidrichMeisner |
| work_keys_str_mv |
AT heidrichmeisnerf transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT martinsgb transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT busserca transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT alhassaniehka transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT feiguinae transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT chiappeg transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT andaev transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy AT dagottoe transportthroughquantumdotsacombineddmrgandembeddedclusterapproximationstudy |
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