Applying Adaptive Time-Dependent DMRG to Calculate the Conductance of Strongly Correlated Nanostructures

TL;DR

This paper introduces an adaptive time-dependent DMRG method to accurately compute zero-temperature conductance in strongly correlated nanostructures, including quantum dots and molecular conductors, by simulating current flow after applying a small bias.

Contribution

The paper presents a novel adaptive time-dependent DMRG approach for calculating conductance in nanostructures, effectively handling interactions and finite biases.

Findings

Excellent agreement with exact results in non-interacting cases

Quantitative reproduction of conductance and density-of-states in interacting quantum dots

Method extends to finite bias voltages and can include lead interactions

Abstract

A procedure based on the recently developed ``adaptive'' time-dependent density-matrix-renormalization-group (DMRG) technique is presented to calculate the zero temperature conductance of nanostructures, such as a quantum dots (QD's) or molecular conductors, when represented by a small number of active levels. The leads are modeled using non-interacting tight-binding Hamiltonians. The ground state at time zero is calculated at zero bias. Then, a small bias is applied between the two leads, the wave-function is DMRG evolved in time, and currents are measured as a function of time. Typically, the current is expected to present periodicities over long times, involving intermediate well-defined plateaus that resemble steady states. The conductance can be obtained from those steady-state-like currents. To test this approach, several cases of interacting and non-interacting systems have been studied. Our results show excellent agreement with exact results in the non-interacting case. More importantly, the technique also reproduces quantitatively well-established results for the conductance and local density-of-states in both the cases of one and two coupled interacting QD's. The technique also works at finite bias voltages, and it can be extended to include interactions in the leads.