We have developed new state of the art density matrix renormalization group (DMRG) and transport codes, which can deal with large electron systems with interaction. Right two figures represent some results we obtained with our collaborators. On the right side, top panel shows our quantum phase diagram for Haldane honeycomb model with spin orbit interaction. It shows that using gate voltage V one can tune into quantum Hall effect (QAHE) by splitting quantum spin Hall effect (QSHE) for system without time reversal symmetry. Bottom panel shows the entanglement gap extrapolates to finite value at thermodynamic limit demonstrating topological order of the 5/2 system. A group of students have been studying condensed matter theory through research projects. Such activities are important in training students for their future PhD studies.
