Impurity effects in interacting quantum many-body systems

Impurities have a wide range of effects in interacting quantum many-body systems. They can interplay with interactions and lead to new electronic states of matter. They can also serve as a probe of an "intrinsic" many-body system. In this thesis, we consider the effects of impurities in three quantum many-body systems. First, we study the transport properties of a two-dimensional interacting electronic system with dilute quenched disorder. We find that the ground state is in fact a metallic state and in-plane magnetic-field can drive it to an insulating one. Second, we address the orthogonality catastrophe in Bose-Einstein condensate with a local impurity at its center. It is shown that the orthogonality effect in a Bose system has a stretched-exponential form, stronger than the algebraic orthogonality of a Fermi counterpart. The corresponding absorption spectrum is also determined. Finally, we analyze the effects of a spin resonance mode on the scattering tunneling microscopy(STM) spectra of a d-wave superconductor near a potential scattering center. We identify a counterintuitive two-unit-cell spatial modulation, at o ≃ +/-(Delta0 + O0)/h, where Delta 0 is the energy gap and O0 is the resonance mode energy. This effect can be tested by the Fourier-transformed STM technique.