Electron Interactions in Finite Size Systems

This thesis explores aspects of the interacting electron problem in systems of finite size. A numerical renormalization group technique based on Wilson's momentum shell method is presented for interacting, finite fermi systems. Results for small fullerene analogs show that the method is quite accurate to moderate values of the electron repulsion, and qualitatively better than other approximation methods. The method has potential applicability far beyond the fullerenes. The effects of electron interactions on the persistent current of one dimensional disordered rings are also studied. We present numerical results for the first order contribution in interactions to the persistent current for tight-binding electrons with on-site repulsive interactions. We find that the persistent current is always enhanced by the interactions, with the largest enhancement occurring for moderate disorder. Analytic arguments supporting these results in the limits of very weak and strong disorder are also given.