Applying Time-dependent DMRG to Calculate the Conductance of Nanostructures

DMRG provides a powerful tool to study quantum 1D systems. We present a detailed procedure for applying the recently developed time-dependent DMRG to calculate the conductance of nanostructures, such as quantum dots (QD's). The leads are modelled using 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 evolved in time and the current is measured as a function of time. Typically, the current saturates at a steady state after a short period of time. The conductance is obtained from the steady-state current. To test this approach We study several cases of interacting and non-interacting systems. Our results show excellent agreement with the exact results in the non-interacting case. We also reproduce quantitatively the well-established results in the case of one interacting QD and two coupled interacting QD's. [1] K. A. Al-Hassanieh {\it et al}, in preparation. [2] Steven R. White and Adrian E. Feiguin, Phys. Rev. Lett. {\bf 93}, 076041 (2004).