Eur. Phys. J. B (2012) 85: 271
https://doi.org/10.1140/epjb/e2012-30123-2

Regular Article

Symmetry-protected quantum phase transition in topological insulators

¹ Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² Department of Physics, Beijing Normal University, Beijing 100875, P.R. China

^a e-mail: liulf@mail.bnu.edu.cn

Received: 10 February 2012
Received in final form: 18 April 2012
Published online: 6 August 2012

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.