Quantum Transport in Strongly Correlated Systems: A Density Matrix Renormalization Group Study

In the past decade there has been a trend towards studying ever smaller devices. Improved experimental techniques have made new experiments possible, one class of which is electron transport through molecules and artificially manufactured structures like quantum dots. In this type of systems screening plays a much less significant role than in bulk systems due to the reduced size of the objects, therefore making it necessary to consider the importance of correlations between electrons. The work presented in this thesis deals with quantum transport through strongly correlated systems using the density matrix renormalization group (DMRG) method. We present two DMRG setups for calculating the linear conductance of strongly correlated nanostructures in the infinitesimal source-drain voltage regime. The first setup describes the leads by modified real-space tight-binding chains, whereas the second describes the leads in momentum-space. We benchmark each of these schemes against exact Greens function results for the conductance in the non-interacting limit, thus demonstrating the accuracy of the lead descriptions. We first use the DMRG implementations to calculate the conductance of an interacting spinless resonant 7 site chain, studying the effect of repulsive interaction inside the chain. We demonstrate that both weak and strong interactions inside the chain lead to Coulomb blockade renormalization of the resonances in the conductance spectrum. Additionally the strongly interacting case sharpens the resonances significantly, such that strong interaction inside the chain tends to suppress the off-resonance transport. Next we consider interacting resonant level models, studying the effect of repulsive interaction on the contact links. We demonstrate that even a small leak of the interaction in the system onto the contact links leads to a strong enhancement of the off-resonance transport, and further that this behavior is non-monotonic. By considering both a single level model and short interacting chains we demonstrate that the off-resonance transport enhancement is stronger than the corresponding suppression when having the interaction inside the chain, and conjecture that the enhancement by interacting contacts is universal. This result challenges the commonly used division between interacting transport region and non-interacting leads, and shows that care should be taken when making this partitioning, particularly regarding the interaction. Finally we consider a spintronics model known as the ferromagnetic Anderson model with an applied magnetic field. The model uses spin-polarized leads and the magnetic field is applied to the transport level at an angle with the direction of polarization. Thus both coherence and correlation effects are important in this model, and the methods applied should be able to handle both these effects rigorously. We present the DMRG setup for this model and benchmark against existing Greens function results for the model. Then we present initial DMRG results demonstrating the ability of the DMRG setup to provide accurate results for this model. We discuss the effects of the various parameters in the model, and finally compare perturbative results in the cotunneling regime with the DMRG results, and thereby quantitatively confirm the range of validity of the perturbative approach.