(I) Topological characterization of metal-insulator transitions in low dimensions and new matter of states in strongly correlated electron systems

Recently, we have systematically studied 2D MITs by using the topological characterization in terms of the first Chern number, including the random-magnetic-field system, the spin-orbital coupling system, and the IQHE in weak magnetic field mentioned before. Our studies indicate a unified topological picture for 2D MITs in non-interacting electron systems with the Anderson localization corresponding to the case of trivial topology.

We have also examined the issue if the observed MIT phenomenon is a true quantum phase transition (QPT) at $T=0$. By performing a series of numerical studies on several well-known quantum phase transitions, we demonstrated that there is a universal scaling form of longitudinal resistance in the quantum critical
region which is satisfied by all these well-known QPTs (including 3D Anderson transitions in different symmetry class, the IQHE plateau to insulator transition). In particular, we found that the experimental B=0 MIT data can also well fit the same universal curve which strongly suggests that it be a $T=0$ QPT [Phys. Rev. Lett, {\bf 83}, 144 (1999)]. Currently, I am also studying this problem analytically by directly mapping the interacting Hamiltonian with spin degrees on to a random-flux effective Hamiltonian with spatially correlations generated from the spin-spin correlations. By studying the effective model numerically, we have found a two-branch scaling typical for a MIT. Further investigation along this line is still underway.