Symmetry protected topological phases of matter

Abstract

matching condition [11][12][13].It is quite difficult to scrutinize nonperturbatively interacting systems, but the 't Hooft anomaly matching condition can be applied to those systems, and possible phases can be constrained.Nowadays, our understanding of the SPT phases has been so developed that applications of the anomaly matching condition can cover systems with finite groups and/or extending objects [14][15][16].In this way, the concept of the topological phases has been essential by now in a wide range of physics, particularly in elementary particle physics, condensed matter physics, and statistical mechanics, as mentioned in the beginning.This special section is a collection of papers related to the topological aspects of physics including the topological phases.We would like to express our sincere gratitude to all the authors who made excellent contributions.