1) We have developed a numerical method to calculate charge and spin topological chern number and drag Hall conductance. Such calculations allow us to explore properties of quantum phase transitions in double layer quantum Hall systems as well as other strongly correlated electron system. Phys. Rev. Lett. 91, 116802 (2003)

2) Based on topological Chern number calculation, we have mapped out the evolution of Fractional quantum Hall effect in the presence of random disorder potential. Phys. Rev. Lett. 90, 256802 (2003)

Supported by National Science Foundation(NSF), American Chemical Society and Research Corporation.