Bosonic Topological Insulators and Paramagnets: a view from cobordisms
نویسنده
چکیده
We classify Bosonic Topological Insulators and Paramagnets in D ≤ 4 spatial dimensions using the cobordism approach. For D < 4 we confirm that the only such phase which does not fit into the group cohomology classification is the 3D Bosonic Topological Insulator protected by time-reversal symmetry whose surface admits an all-fermion topologically ordered state. ForD = 4 there is a unique ”beyond group cohomology” phase. It is protected by gravitational anomalies of the boundary theory and is stable without any additional symmetry.
منابع مشابه
Topological paramagnetism in frustrated spin-1 Mott insulators
Time-reversal-protected three-dimensional (3D) topological paramagnets are magnetic analogs of the celebrated 3D topological insulators. Such paramagnets have a bulk gap and no exotic bulk excitations, but have non-trivial surface states protected by symmetry. We propose that frustrated spin-1 quantum magnets are a natural setting for realizing such states in three dimensions. We describe a phy...
متن کاملClassification of interacting electronic topological insulators in three dimensions.
A fundamental open problem in condensed-matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are six interacting electronic topological insulators that have no noninteracting counterpart. Combined with the previously known band insulators, these produce a total of eight topologica...
متن کاملSymmetry-protected topological orders in interacting bosonic systems.
Symmetry-protected topological (SPT) phases are bulk-gapped quantum phases with symmetries, which have gapless or degenerate boundary states as long as the symmetries are not broken. The SPT phases in free fermion systems, such as topological insulators, can be classified; however, it is not known what SPT phases exist in general interacting systems. We present a systematic way to construct SPT...
متن کاملSymmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in...
متن کاملTopological Bose-Mott insulators in a one-dimensional optical superlattice.
We study topological properties of the Bose-Hubbard model with repulsive interactions in a one-dimensional optical superlattice. We find that the Mott insulator states of the single-component (two-component) Bose-Hubbard model under fractional fillings are topological insulators characterized by a nonzero charge (or spin) Chern number with nontrivial edge states. For ultracold atomic experiment...
متن کامل