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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Guardado en:
Detalles Bibliográficos
Publicado: 2009
Materias:
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
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v67_n4_p527_HeidrichMeisner
http://hdl.handle.net/20.500.12110/paper_14346028_v67_n4_p527_HeidrichMeisner
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_14346028_v67_n4_p527_HeidrichMeisner
record_format dspace
spelling paper:paper_14346028_v67_n4_p527_HeidrichMeisner2023-06-08T16:14:36Z Transport through quantum dots: A combined DMRG and embedded-cluster approximation study 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v67_n4_p527_HeidrichMeisner 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
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.
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
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_14346028_v67_n4_p527_HeidrichMeisner
http://hdl.handle.net/20.500.12110/paper_14346028_v67_n4_p527_HeidrichMeisner
_version_ 1768544333882982400

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