Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
read the original abstract
It is well known that (1+1)-D bosonic symmetry-protected topological (SPT) phases with symmetry group $G$ can be identified by the projective representation of the symmetry at the edge. Here, we generalize this result to higher dimensions. We assume that the representation of the symmetry on the spatial edge of a ($d+1$)-D SPT is /local/ but not necessarily /on-site/, such that there is an obstruction to its implementation on a region with boundary. We show that such obstructions are classified by the cohomology group $H^{d+1}(G, U(1))$, in agreement with the classification of bosonic SPT phases proposed in [Chen et al, Science 338, 1604 (2012)]. Our analysis allows for a straightforward calculation of the element of $H^{d+1}(G, U(1))$ corresponding to physically meaningful models such as non-linear sigma models with a theta term in the action. SPT phases outside the classification of Chen et al are those in which the symmetry cannot be represented locally on the edge. With some modifications, our framework can also be applied to fermionic systems in (2+1)-D.
This paper has not been read by Pith yet.
Forward citations
Cited by 4 Pith papers
-
Constructing Bulk Topological Orders via Layered Gauging
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
-
Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
-
When Symmetries Twist: Anomaly Inflow on Monodromy Defects
Monodromy defects for anomalous symmetries are defined as domain walls between symmetry generators and anomaly-induced topological orders, resulting in protected chiral edge modes and adiabatic pumping of gapless degr...
-
Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.