DMRG evaluation of the Kubo formula —Conductance of strongly interacting quantum systems

¹ MIC - Department of Micro and Nanotechnology, Technical University of Denmark Building 345E - DK-2800 Kgs. Lyngby, Denmark
² TKM - Institut für Theorie der Kondensierten Materie, Universität Karlsruhe Wolfgang-Gaede-Str. 1, D-76128 Karlsruhe, Germany

Received: 8 June 2005
Accepted: 16 November 2005

Abstract

In this paper we present a novel approach combining linear response theory (Kubo) for the conductance and the Density Matrix Renormalization Group (DMRG). The system considered is one-dimensional and consists of non-interacting tight-binding leads coupled to an interacting nanostructure via weak links. Electrons are treated as spinless fermions and two different correlation functions are used to evaluate the conductance. Exact diagonalization calculations in the non-interacting limit serve as a benchmark for our combined Kubo and DMRG approach in this limit. Including both weak and strong interaction we present DMRG results for an extended nanostructure consisting of seven sites. For the strongly interacting structure a simple explanation of the position of the resonances is given in terms of hard-core particles moving freely on a lattice of reduced size.