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

TL;DR

This paper introduces a new method combining Kubo linear response theory with DMRG to evaluate conductance in one-dimensional quantum systems with interactions, validated against exact results and applied to complex nanostructures.

Contribution

The paper develops a novel combined Kubo-DMRG approach for calculating conductance in interacting quantum systems, extending previous methods to strongly correlated nanostructures.

Findings

Benchmarking against exact diagonalization in non-interacting limit

Successful application to seven-site strongly interacting nanostructure

Resonance positions explained by hard-core particle model

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.