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Obtaining the Full Counting Statistics of Correlated Nanostructures from Time Dependent Simulations

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High Performance Computing in Science and Engineering '11

Abstract

Transport properties of strongly interacting quantum systems are a major challenge in todays condensed matter theory. In our project we apply the density matrix renormalization group method to study transport properties of quantum devices attached to metallic leads.

To this end we have developed two complementary approaches to obtain conductance of a structure coupled to left and right leads. First we use the Kubo approach to obtain linear conductance. Combined with leads described in momentum space we have obtained high resolution in energy. The second approach is based on simulating the time evolution of an initial state with a charge imbalance. In cooperation with Edouard Boulat and Hubert Saleur we have been able to show that our approach is in excellent agreement with analytical calculations in the framework of the Bethe ansatz. This agreement is remarkable as the numerics is carried out in a lattice model, while the analytical result is based on field theoretical methods in the continuum. Therefore we have to introduce a scale T B to compare the field theoretical result to our numerics. Remarkably, at the so called self-dual point the complete regularization can be expressed by a single number, even for arbitrary contact hybridization t′. Most strikingly we proved the existence of a negative differential conductance regime even in this simplistic model of a single resonant level with interaction on the contact link.

In an extension of this approach we presented results for current-current correlations, including shot noise, based on our real time simulations in our last report. In this report we extend this scheme in order to access the cumulant generating function of the electronic transport within the interacting resonant level model at its self-dual point.

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Author information

Authors and Affiliations

  1. Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344, Eggenstein-Leopoldshafen, Germany

    Peter Schmitteckert

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  1. Peter Schmitteckert
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Editors and Affiliations

  1. Zentrum für Informationsdienste und, Hochleistungsrechnen (ZIH), TU Dresden, Helmholtzstr. 10, Dresden, 01069, Germany

    Wolfgang E. Nagel

  2. , Abt. Angewandte Mathematik, Universität Freiburg, Hermann-Herder-Str. 10, Freiburg, 79104, Germany

    Dietmar B. Kröner

  3. , Höchstleistungsrechenzentrum, Universität Stuttgart, Nobelstraße 19, Stuttgart, 70569, Germany

    Michael M. Resch

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Schmitteckert, P. (2012). Obtaining the Full Counting Statistics of Correlated Nanostructures from Time Dependent Simulations. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23869-7_12

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