A study of disorder effects in quantum systems

Disorder plays various roles in physical systems. The existence of randomness can dramatically alter, or even dominate, the physics of the corresponding pure system. This dissertation provides a systematic study of the disorder in a set of four problems.;In Chapter 2, we consider the dynamics of a spin-1/2 Ising model in a random transverse magnetic field. By explicitly calculating the dynamic structure factor S(k, o) at T = 0 we demonstrate that there exists a zero energy non-dispersing mode for a binary disorder field. This work is also of experimental relevance to neutron scattering measurements in LiHoF4.;In Chapter 3 we study the non-analyticity of von Neumann entropy in quantum phase transitions in disordered systems. The scaling behavior of the von Neumann entropy is shown due to the multi-fractal nature of the wave functions close to the phase transitions. Numerical computations performed in the localization-delocalization transition in the 3-D Anderson model and in the plateau-to-plateau transitions in an integer quantum Hall system confirm this relationship.;In Chapter 4, we investigate the critical phenomena in the disordered lowest Landau level in graphene. Four types of disorder fields enter in this low energy relativistic theory. A continuously varying critical exponent depending on disorder is found. In Chapter 5, we demonstrate that bond disorder in graphene can produce a plateau-like feature centered at the filling fraction nu f = 0, while the longitudinal conductance is nonzero in the same region.;Chapter 6 and Chapter 7 focus on the d-density wave order in underdoped high-Tc superconductors. The Fermi surface reconstructions and their consequences on quantum oscillation experiments are discussed in Chapter 6. In Chapter 7 we demonstrate that the presence of correlated disorder makes electron pockets invisible in Angle-Resolved Spectroscopy measurements. In addition, we show that the vortex scattering in the mixed state wipes out the signature of hole pockets in the Shubnikov-de Haas oscillations.