TOPOLOGICAL QUANTUM PHASE TRANSITION BETWEEN QUANTUM SPIN HALL STATE AND QUANTUM ANOMALOUS HALL STATE

In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities, and the number of zero mode on a π-flux). We find that at the topological quantum phase transitions (TQPTs), the topological "order parameter" — spin Chern number will jump. And since the masses of the nodal fermions will change sign, the third derivative of ground-state energy is nonanalytic. In addition, we discuss the finite temperature properties and the stability of the TQPTs.