2014/12/31 by Chenjie Wang, Michael Levin · 3 citations
Mathematics · Physics and Astronomy · #Abelian group #Black Holes and Theoretical Physics #Cohomology #Combinatorics #Conjecture #Gauge theory #Geometry #Group (periodic table) #Group cohomology #Lattice (music) #Mathematics #Physics #Pure mathematics #Quantum many-body systems #Quantum mechanics #Symmetry (geometry) #Symmetry group #Theoretical physics #Topological Materials and Phenomena #Topology (electrical circuits) #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.91.165119
published as Phys. Rev. B 91, 165119 (2015) · 28 pages, 8 figures. Published version
openalex publication_date 2015/04/15 · arxiv created 2015/04/17 · arxiv updated 2015/04/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
According to a recent theoretical conjecture for a classification of symmetry protected topological (SPT) phases which can arise in a collection of lattice boson models called group cohomology models, each model belongs to a distinct SPT phase, and each SPT phase can be realized by a model. Here the authors show that for SPT phases with symmetry groups that are finite, Abelian, and unitary, each group cohomology model can be characterized by a unique set of topological invariants and therefore belongs to a distinct SPT phase. In two dimensions it is further shown that the complete set of group cohomology models accounts for all SPT phases, while in three dimensions evidence pointing toward such a proof is found.