Residual conductance of correlated one-dimensional nanosystems: A numerical approach

TL;DR

This paper introduces a numerical method using DMRG to determine the residual conductance of correlated one-dimensional systems by analyzing persistent currents in a ring with leads, extending previous approaches to arbitrary fillings and disordered systems.

Contribution

The paper develops and extends a DMRG-based numerical approach to calculate residual conductance in correlated 1D systems, including disordered and arbitrary filling cases.

Findings

Interacting systems behave as non-interacting scatterers with an interaction-dependent transmission.

The method accurately scales with lead size to determine conductance.

Repulsive interactions can enhance transport in disordered systems.

Abstract

We study a method to determine the residual conductance of a correlated system by means of the ground-state properties of a large ring composed of the system itself and a long non-interacting lead. The transmission probability through the interacting region and thus its residual conductance is deduced from the persistent current induced by a flux threading the ring. Density Matrix Renormalization Group techniques are employed to obtain numerical results for one-dimensional systems of interacting spinless fermions. As the flux dependence of the persistent current for such a system demonstrates, the interacting system coupled to an infinite non-interacting lead behaves as a non-interacting scatterer, but with an interaction dependent elastic transmission coefficient. The scaling to large lead sizes is discussed in detail as it constitutes a crucial step in determining the conductance. Furthermore, the method, which so far had been used at half filling, is extended to arbitrary filling and also applied to disordered interacting systems, where it is found that repulsive interaction can favor transport.