Symmetry protection of quantum phase transitions in honeycomb lattice

Based on an analytical model of topological insulator, we present the quantum phase transitions of topological insulators with different symmetries by calculating their phase diagrams and edgestates. In particular, we show the symmetry protection nature of the topological quantum phase transitions. Topological quantum phase transitions cannot be classified by symmetries. However, the symmetry of the system plays an important role, where different topological quantum phase transitions are protected by different global symmetries.