Quantum phase transitions in two-dimensional electron systems under strong magnetic field

In this dissertation various aspects of quantum phase transitions in two dimensional systems under strong magnetic field are studied theoretically. We present our results on universal scaling of strong field localization in an integer quantum Hall liquid, gauge field fluctuation induced composite fermion localization in the fractional quantum Hall regime and optical properties of quantum Wigner crystal induced by a strong magnetic field.;This dissertation is divided into three parts:;At first, I will discuss localization properties of a disordered two dimensional electron system under strong magnetic fields. I will present our theoretical investigation on the scaling and universality in the integer quantum Hall plateau transitions.;Secondly, I will discuss the interplay between electron-electron interaction and random impurity potential. I will present our theory on the gauge field fluctuation induced composite fermion localization in the fractional quantum Hall regime.;Finally, I will discuss the elementary properties of a strong magnetic field induced two dimensional quantum Wigner crystal. I will present our theory of photoluminescence from Wigner crystal including both mean-field results and phonon shakeup effects.