Boundary multifractality and conformal invariance at localization -delocalization transitions

Disordered non-interacting electronic systems can undergo transitions between de-localized and localized single particle wavefunctions as their energy is varied. In this thesis, multifractal behavior of wavefunctions at such transitions near sample boundaries and corners and its relation to conformal invariance in two dimensions are studied. The concepts of boundary and corner multifractality are formulated and the influence of boundaries on various observables is analyzed from a general perspective. These ideas are then applied to a number of localization-delocalization (LD) transitions, each occurring in a single-particle system with a distinct dimensionality and symmetry. These analyses reveal a number of expected as well as novel features some of which are specific to the systems studied while others are common to all LD transitions. Study of boundary multifractality has a direct bearing on the nature of the unknown critical theories for LD transitions. In addition, the behavior of entanglement entropy near LD transitions has been analyzed and its scaling behavior illustrated in a few model systems.