Regensburg 2010 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 27: CE: Poster Session
TT 27.62: Poster
Wednesday, March 24, 2010, 14:00–18:00, Poster D1
Matrix product state approach for a two-lead, multi-level Anderson model — •Andreas Holzner, Andreas Weichselbaum, and Jan von Delft — Lehrstuhl für Theoretische Festkörperphysik, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universität München, Theresienstraße 37, D-80333 München, Germany
We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own Wilson chain, instead of using a single Wilson chain for all species together, we achieve a very significant reduction in the numerical resources required to obtain reliable results, as illustrated for the occupation for a spinfull two-lead 4-level Anderson model. Moreover, we show that it is possible to find a new "optimal" lead basis, obtained via a unitary transformation of the type cα kσ → Uαβcβ kσ (where α and β label distinct leads), in which lead degrees of freedom on different Wilson chains are effectively decoupled from each other for all but the first few sites of each chain. This new basis turns out to also diagonalize the scattering matrix for the leads. We demonstrate this for a spinless two-lead, 4-level Anderson model, presenting DMRG-results for the mutual information between two sites located far apart on different Wilson chains, and NRG results for the scattering matrix.