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Koller, S. ; Leijnse, M. ; Wegewijs, M. R. ; Grifoni, Milena

Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory

Koller, S., Leijnse, M., Wegewijs, M. R. und Grifoni, Milena (2010) Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory. Phys. Rev. B 82 (23), S. 235307.

Veröffentlichungsdatum dieses Volltextes: 07 Mrz 2011 09:28
Artikel
DOI zum Zitieren dieses Dokuments: 10.5283/epub.20039


Zusammenfassung

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate ...

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate approach based on the T-matrix (TM). Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences (nondiagonal elements of the density matrix) between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary (zero-frequency) limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.



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Details

DokumentenartArtikel
Titel eines Journals oder einer ZeitschriftPhys. Rev. B
Verlag:AMER PHYSICAL SOC
Ort der Veröffentlichung:COLLEGE PK
Band:82
Nummer des Zeitschriftenheftes oder des Kapitels:23
Seitenbereich:S. 235307
DatumDezember 2010
InstitutionenPhysik > Institut für Theoretische Physik > Lehrstuhl Professor Grifoni > Arbeitsgruppe Milena Grifoni
ThemenverbundNicht ausgewählt
Identifikationsnummer
WertTyp
10.1103/PhysRevB.82.235307DOI
Stichwörter / KeywordsRENORMALIZATION-GROUP METHOD; SINGLE-ELECTRON TRANSISTOR; CARBON NANOTUBE; MASTER EQUATION; KONDO PROBLEM; LOGIC GATES; MOLECULE; SPECTROSCOPY; RELAXATION; DERIVATION;
Dewey-Dezimal-Klassifikation500 Naturwissenschaften und Mathematik > 530 Physik
StatusVeröffentlicht
BegutachtetJa, diese Version wurde begutachtet
An der Universität Regensburg entstandenJa
URN der UB Regensburgurn:nbn:de:bvb:355-epub-200395
Dokumenten-ID20039

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