79 research outputs found
Flux-fusion anomaly test and bosonic topological crystalline insulators
We introduce a method, dubbed the flux-fusion anomaly test, to detect certain
anomalous symmetry fractionalization patterns in two-dimensional symmetry
enriched topological (SET) phases. We focus on bosonic systems with Z2
topological order, and symmetry group of the form G = U(1) G', where
G' is an arbitrary group that may include spatial symmetries and/or time
reversal. The anomalous fractionalization patterns we identify cannot occur in
strictly d=2 systems, but can occur at surfaces of d=3 symmetry protected
topological (SPT) phases. This observation leads to examples of d=3 bosonic
topological crystalline insulators (TCIs) that, to our knowledge, have not
previously been identified. In some cases, these d=3 bosonic TCIs can have an
anomalous superfluid at the surface, which is characterized by non-trivial
projective transformations of the superfluid vortices under symmetry. The basic
idea of our anomaly test is to introduce fluxes of the U(1) symmetry, and to
show that some fractionalization patterns cannot be extended to a consistent
action of G' symmetry on the fluxes. For some anomalies, this can be described
in terms of dimensional reduction to d=1 SPT phases. We apply our method to
several different symmetry groups with non-trivial anomalies, including G =
U(1) X Z2T and G = U(1) X Z2P, where Z2T and Z2P are time-reversal and d=2
reflection symmetry, respectively.Comment: 18+13 pages, 4 figures. Significant changes to introduction, and
other changes to improve presentation. Title shortene
Symmetry fractionalization and anomaly detection in three-dimensional topological phases
In a phase with fractional excitations, topological properties are enriched
in the presence of global symmetry. In particular, fractional excitations can
transform under symmetry in a fractionalized manner, resulting in different
Symmetry Enriched Topological (SET) phases. While a good deal is now understood
in regarding what symmetry fractionalization patterns are possible, the
situation in is much more open. A new feature in is the existence of
loop excitations, so to study SET phases, first we need to understand how
to properly describe the fractionalized action of symmetry on loops. Using a
dimensional reduction procedure, we show that these loop excitations exist as
the boundary between two SET phases, and the symmetry action is
characterized by the corresponding difference in SET orders. Moreover, similar
to the case, we find that some seemingly possible symmetry
fractionalization patterns are actually anomalous and cannot be realized
strictly in . We detect such anomalies using the flux fusion method we
introduced previously in . To illustrate these ideas, we use the
gauge theory with global symmetry as an example, and enumerate and
describe the corresponding SET phases. In particular, we find four
non-anomalous SET phases and one anomalous SET phase, which we show can be
realized as the surface of a system with symmetry protected topological
order.Comment: 19 pages, 8 figure
- β¦