Symmetry-Protected Topological Orders in Interacting Bosonic Systems

Symmetry Semantics Topological insulators (TIs) are characterized by boundary states that are protected by time-reversal symmetry. A systematic study of this, and other symmetry-protected states, is possible in noninteracting systems, but complications arise when interactions are present. Chen et al. (p. 1604 ; see the Perspective by Qi ) used group cohomology theory to predict symmetry-protected phases of interacting bosons. The analysis enabled the generalization of a known result in one dimension by using a path-integral formulation and suggests the existence of three counterparts of TIs in three dimensions, and one in two dimensions, as well as phases protected by other symmetries. The formalism is applicable to any symmetry group and dimension and is valid for interactions of arbitrary strength.