Abstract
In this paper, based on the lattice model of a topological insulator, we study the quantum phase transitions of topological insulators with different symmetry by calculating their phase diagrams and topological invariants. In particular, we investigate the symmetry-protected nature of the topological quantum phase transitions: topological quantum phase transitions can not be classified by symmetries. However, the symmetry of the system plays an important role: different topological quantum phase transitions are protected by different (global) symmetries and then described by different topological invariants.
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