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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
| Dokumentenart | Artikel | ||||
| Titel eines Journals oder einer Zeitschrift | Phys. Rev. B | ||||
| Verlag: | AMER PHYSICAL SOC | ||||
|---|---|---|---|---|---|
| Ort der Veröffentlichung: | COLLEGE PK | ||||
| Band: | 82 | ||||
| Nummer des Zeitschriftenheftes oder des Kapitels: | 23 | ||||
| Seitenbereich: | S. 235307 | ||||
| Datum | Dezember 2010 | ||||
| Institutionen | Physik > Institut für Theoretische Physik > Lehrstuhl Professor Grifoni > Arbeitsgruppe Milena Grifoni | ||||
| Themenverbund | Nicht ausgewählt | ||||
| Identifikationsnummer |
| ||||
| Stichwörter / Keywords | RENORMALIZATION-GROUP METHOD; SINGLE-ELECTRON TRANSISTOR; CARBON NANOTUBE; MASTER EQUATION; KONDO PROBLEM; LOGIC GATES; MOLECULE; SPECTROSCOPY; RELAXATION; DERIVATION; | ||||
| Dewey-Dezimal-Klassifikation | 500 Naturwissenschaften und Mathematik > 530 Physik | ||||
| Status | Veröffentlicht | ||||
| Begutachtet | Ja, diese Version wurde begutachtet | ||||
| An der Universität Regensburg entstanden | Ja | ||||
| URN der UB Regensburg | urn:nbn:de:bvb:355-epub-200395 | ||||
| Dokumenten-ID | 20039 |
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