14,517 research outputs found
Universal symmetry-protected topological invariants for symmetry-protected topological states
Symmetry-protected topological (SPT) states are short-range entangled states
with a symmetry G. They belong to a new class of quantum states of matter which
are classified by the group cohomology in
d-dimensional space. In this paper, we propose a class of symmetry- protected
topological invariants that may allow us to fully characterize SPT states with
a symmetry group G (ie allow us to measure the cocycles in
that characterize the SPT states). We give
an explicit and detailed construction of symmetry-protected topological
invariants for 2+1D SPT states. Such a construction can be directly generalized
to other dimensions.Comment: 12 pages, 11 figures. Added reference
Polar Coding for the Cognitive Interference Channel with Confidential Messages
In this paper, we propose a low-complexity, secrecy capacity achieving polar
coding scheme for the cognitive interference channel with confidential messages
(CICC) under the strong secrecy criterion. Existing polar coding schemes for
interference channels rely on the use of polar codes for the multiple access
channel, the code construction problem of which can be complicated. We show
that the whole secrecy capacity region of the CICC can be achieved by simple
point-to-point polar codes due to the cognitivity, and our proposed scheme
requires the minimum rate of randomness at the encoder
Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
We study the quantized topological terms in a weak-coupling gauge theory with
gauge group and a global symmetry in space-time dimensions. We
show that the quantized topological terms are classified by a pair ,
where is an extension of by and an element in group
cohomology \cH^d(G,\R/\Z). When and/or when is finite, the
weak-coupling gauge theories with quantized topological terms describe gapped
symmetry enriched topological (SET) phases (i.e. gapped long-range entangled
phases with symmetry). Thus, those SET phases are classified by
\cH^d(G,\R/\Z), where . We also apply our theory to a simple case
, which leads to 12 different SET phases in 2+1D, where
quasiparticles have different patterns of fractional quantum numbers
and fractional statistics. If the weak-coupling gauge theories are gapless,
then the different quantized topological terms may describe different gapless
phases of the gauge theories with a symmetry , which may lead to different
fractionalizations of quantum numbers and different fractional statistics
(if in 2+1D).Comment: 13 pages, 2 figures, PRB accepted version with added clarification on
obtaining G_s charge for a given PSG with non-trivial topological terms.
arXiv admin note: text overlap with arXiv:1301.767
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