Conductance and Noise Correlations of Correlated Nanostructures

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 (DMRG) method (White 1992, 1993; Peschel et al. 1999; Noack and Manmana 2005; Hallberg 2006; Schollwöck 2005) to study transport properties (Schmitteckert 2004; Schmitteckert and Schneider 2006; Schmitteckert 2007; Ulbricht and Schmitteckert 2008; Branschädel 2009) 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 (Bohr et al. 2006) to obtain linear conductance. Combined with leads described in momentum space (Bohr and Schmitteckert 2007; Schmitteckert 2010) we have obtained high resolution in energy. In this report we extend the results based on the Kubo approach to systems with degenerate orbitals. The second approach is based on simulating the time evolution (Ulbricht and Schmitteckert 2009, 2010; Ulbricht et al. 2010) of an initial state with a charge imbalance (Branschädel 2010). In a 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 (Boulat et al. 2009). 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 (NDC) regime even in this simplistic model of a single resonant level with interaction on the contact link. In an extension of this approach we present results for current-current correlations, including shot noise, based on our real time simulations.