Density-matrix renormalization group method for the conductance of one-dimensional correlated systems using the Kubo formula

TL;DR

This paper presents an improved DMRG-based method to accurately compute the zero-temperature conductance of one-dimensional correlated systems using the Kubo formula, validated on a spinless fermion model.

Contribution

The authors develop a dynamical DMRG approach to evaluate the Kubo formula for conductance, enabling precise extrapolation to the thermodynamic limit for 1D correlated systems.

Findings

Successfully reproduces Luttinger liquid conductance renormalization

Captures universal effects of single barriers

Demonstrates resonant tunneling in double barrier systems

Abstract

We improve the density-matrix renormalization group (DMRG) evaluation of the Kubo formula for the zero-temperature linear conductance of one-dimensional correlated systems.The dynamical DMRG is used to compute the linear response of a finite system to an applied AC source-drain voltage, then the low-frequency finite-system response is extrapolated to the thermodynamic limit to obtain the DC conductance of an infinite system. The method is demonstrated on the one-dimensional spinless fermion model at half filling. Our method is able to replicate several predictions of the Luttinger liquid theory such as the renormalization of the conductance in an homogeneous conductor, the universal effects of a single barrier, and the resonant tunneling through a double barrier.