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Abstract

Symmetry-Protected Topological (SPT) phases are, as the name suggests, topological phases without any conventional local order parameter, but distinct from the trivial phase only in the presence of a certain symmetry. Although it was first conceived by Gu and Wen in 2009, its prototypical example, the Haldane gap phase in odd-integer spin chains, was discovered much earlier in the 1980s. As an important part of early studies, Kennedy and
Tasaki introduced a non-local transformation which maps between the Haldane gap phase and a conventional Spontaneous Symmetry Breaking (SSB) phase. The duality picture could have naturally led to the concept of the SPT phases.
In this talk, I will review the concept of SPT phases from the duality point of view, and its historical developments. I will also discuss the recent resurgence of the duality approach inspired by modern field theory formulation. It leads to a systematic construction of SPT phases including a novel variety of “gapless SPT phases”.