Abstract:

Quantum phase transitions (QPT) are argued to play important role in the strongly correlated systems such as high-Tc superconductors, heavy fermions, and quantum Hall systems. The results presented in this dissertation are motivated by numerous experiments and the possibility of novel QPTs in the dissipative and disordered systems.

In Chapter 2, employing a strong coupling renormalization group (RG) analysis we study the phase diagram and quantum critical properties of a resistively shunted Josephson junction array (RSJJA) in one dimension. The RG calculations are performed after mapping the dissipative quantum phase model to an effective two-component sine-Gordon model. We attempt to bridge the phase diagrams obtained from the weak and the strong coupling RG calculations, and discuss the experimental relevance of our theory.

In Chapter 3 we provide a heuristic argument for disorder rounding of a first order quantum phase transition (QPT1 ) into a continuous QPT. For the N -color quantum Ashkin-Teller model in one spatial dimension, employing both weak and strong disorder RG calculations, we have found that for N ? 3, the QPT1 is rounded to a continuous QPT for a limited parameter regime. The emergent quantum critical properties in this parameter regime are governed by the infinite disorder quantum critical point (QCP) of the random transverse field Ising model.

In Chapter 4 we investigate, analytically and numerically, the effects of disorder on the density of states and on the localization properties of the two dimensional relativistic fermions in the lowest Landau level (LLL) of graphene. Employing a supersymmetric technique, we have calculated the exact density of states for various types of disorders for the Cauchy distribution. We use recursive Green's function and transfer matrix techniques to establish the localization-delocalization (LD) transition in the LLL. For some types of disorder we show the LD transition belongs to a different universality class, as compared to the corresponding nonrelativistic problem. For the random hopping we have numerically calculated longitudinal and Hall conductances that show unusual features around the zero energy.