# Density-matrix renormalization group study of the linear conductance in quantum wires coupled to interacting leads or phonons

## TL;DR

This paper extends a density-matrix renormalization group method to study linear conductance in inhomogeneous quantum wires coupled to interacting leads or phonons, demonstrating its effectiveness through various models and comparisons with theoretical predictions.

## Contribution

The authors develop and validate an extended DMRG method for calculating conductance in complex inhomogeneous and phononic quantum systems, including spin and electron-phonon interactions.

## Key findings

- Complex conductance behavior in wires with differing lead interactions.
- Renormalization of conductance by Luttinger parameter remains valid with phonons.
- Method agrees well with Luttinger liquid theory and Bethe Ansatz results.

## Abstract

In a previous paper [J.-M. Bischoff and E. Jeckelmann, Phys. Rev. B 96, 195111 (2017)] we introduced a density-matrix renormalization group method for calculating the linear conductance of one-dimensional correlated quantum systems and demonstrated it on homogeneous spinless fermion chains with impurities. Here we present extensions of this method to inhomogeneous systems, models with phonons, and the spin conductance of electronic models. The method is applied to a spinless fermion wire-lead model, the homogeneous spinless Holstein model, and the Hubbard model. Its capabilities are demonstrated by comparison with the predictions of Luttinger liquid theory combined with Bethe Ansatz solutions and other numerical methods. We find a complex behavior for quantum wires coupled to interacting leads when the sign of the interaction (repulsive/attractive) differs in wire and leads. The renormalization of the conductance given by the Luttinger parameter in purely fermionic systems is shown to remain valid in the Luttinger liquid phase of the Holstein model with phononic degrees of freedom.