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Classification of quantum phases is one of the central problems in statistical mechanics and condensed matter physics. Traditionally, it had been associated to spontaneous symmetry breakings. However, a rich variety of quantum phases without any spontaneous symmetry breaking have been found and dubbed as topological phases. Symmetries can still play an important role even when there is no spontaneous symmetry breaking, as some quantum phases are distinct only in the presence of certain symmetries. I will review the concept of “symmetry-protected topological phases” and then discuss our recent attempts in generalizing the notion of symmetry protection of quantum phases.
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