Adaptive time-dependent density-matrix renormalization-group technique for calculating the conductance of strongly correlated nanostructures

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 quantum dots (QDs) or molecular conductors, when represented by a small number of active levels. The leads are modeled using noninteracting 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 noninteracting systems have been studied. Our results show excellent agreement with exact results in the noninteracting 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 QDs. The technique also works at finite bias voltages, and it can be extended to include interactions in the leads.