Conductance of correlated systems: real-time dynamics in finite systems

TL;DR

This paper reviews numerical methods, especially td-DMRG, for calculating conductance in correlated finite systems, demonstrating their effectiveness through models like IRLM and SIAM, and discussing finite size effects and accuracy enhancements.

Contribution

It provides a detailed overview of numerical techniques for real-time conductance calculations in correlated systems, with new insights into finite size effects and boundary damping methods.

Findings

Successful application of td-DMRG to IRLM and related models

Verification of methods against exact diagonalization in non-interacting limit

Discussion of finite size effects and boundary damping to improve accuracy

Abstract

Numerical time evolution of transport states using time dependent Density Matrix Renormalization Group (td-DMRG) methods has turned out to be a powerful tool to calculate the linear and finite bias conductance of interacting impurity systems coupled to non-interacting one-dimensional leads. Several models, including the Interacting Resonant Level Model (IRLM), the Single Impurity Anderson Model (SIAM), as well as models with different multi site structures, have been subject of investigations in this context. In this work we give an overview of the different numerical approaches that have been successfully applied to the problem and go into considerable detail when we comment on the techniques that have been used to obtain the full I--V-characteristics for the IRLM. Using a model of spinless fermions consisting of an extended interacting nanostructure attached to non-interacting leads, we explain the method we use to obtain the current--voltage characteristics and discuss the finite size effects that have to be taken into account. We report results for the linear and finite bias conductance through a seven site structure with weak and strong nearest-neighbor interactions. Comparison with exact diagonalisation results in the non-interacting limit serve as a verification of the accuracy of our approach. Finally we discuss the possibility of effectively enlarging the finite system by applying damped boundaries and give an estimate of the effective system size and accuracy that can be expected in this case.