Research Projects

The complex interplay of electronic interactions and disorder in two-dimensional (2D) systems could give rise to intriguing modifications to the conclusions of the scaling theory of Anderson localization (AL). Focusing on the role of strong interactions we employ Gutzwiller projections and describe the system as an effective non-interacting system, but with an appropriately modified Hamiltonian. This new Hamiltonian now has renormalized hopping and spatially correlated site disorder. Analyzing physical observables resulting from this Hamiltonian, we propose to investigate how interactions can generate the possibility of a metal insulator transition in two-dimension. We also explore the impact of multi-fractality on correlation functions in systems featuring AL. Finally, we plan to develop the Kernel-polynomial method which aids numerical self-consistency by expressing correlation functions in a rapidly converging series of Chebyshev polynomials. Such a method is expected to overcome a major numerical challenge for a broad class of self-consistent calculations.