Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains

TL;DR

This paper demonstrates that using Wilson chains in time-dependent DMRG simulations significantly improves the accuracy and efficiency of studying Kondo effects in quantum dot transport, enabling smaller system sizes and better results.

Contribution

The authors introduce a modified tDMRG approach using Wilson chains to better capture Kondo physics in quantum dot transport, reducing computational demands.

Findings

Wilson chains improve conductance accuracy in Kondo regime

Enhanced stability of current plateaus at longer times

Effective for finite-bias regimes up to Kondo temperature

Abstract

We apply the adaptive time-dependent Density Matrix Renormalization Group method (tDMRG) to the study of transport properties of quantum-dot systems connected to metallic leads. Finite-size effects make the usual tDMRG description of the Kondo regime a numerically demanding task. We show that such effects can be attenuated by describing the leads by "Wilson chains", in which the hopping matrix elements decay exponentially away from the impurity ($t_n \propto \Lambda^{-n/2}$). For a given system size and in the linear response regime, results for $\Lambda > 1$ show several improvements over the undamped, $\Lambda=1$ case: perfect conductance is obtained deeper in the strongly interacting regime and current plateaus remain well defined for longer time scales. Similar improvements were obtained in the finite-bias regime up to bias voltages of the order of the Kondo temperature. These results show that, with the proposed modification, the tDMRG characterization of Kondo correlations in the transport properties can be substantially improved, while it turns out to be sufficient to work with much smaller system sizes. We discuss the numerical cost of this approach with respect to the necessary system sizes and the entanglement growth during the time-evolution.