2,817 research outputs found
A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
Topological orders are new phases of matter beyond Landau symmetry breaking.
They correspond to patterns of long-range entanglement. In recent years, it was
shown that in 1+1D bosonic systems there is no nontrivial topological order,
while in 2+1D bosonic systems the topological orders are classified by a pair:
a modular tensor category and a chiral central charge. In this paper, we
propose a partial classification of topological orders for 3+1D bosonic
systems: If all the point-like excitations are bosons, then such topological
orders are classified by unitary pointed fusion 2-categories, which are
one-to-one labeled by a finite group and its group 4-cocycle up to group automorphisms. Furthermore, all such 3+1D
topological orders can be realized by Dijkgraaf-Witten gauge theories.Comment: An important new result "Untwisted sector of dimension reduction is
the Drinfeld center of E" is added in Sec. IIIC; other minor refinements and
improvements; 23 pages, 10 figure
A theory of 2+1D fermionic topological orders and fermionic/bosonic topological orders with symmetries
We propose that, up to invertible topological orders, 2+1D fermionic
topological orders without symmetry and 2+1D fermionic/bosonic topological
orders with symmetry are classified by non-degenerate unitary braided
fusion categories (UBFC) over a symmetric fusion category (SFC); the SFC
describes a fermionic product state without symmetry or a fermionic/bosonic
product state with symmetry , and the UBFC has a modular extension. We
developed a simplified theory of non-degenerate UBFC over a SFC based on the
fusion coefficients and spins . This allows us to obtain a list
that contains all 2+1D fermionic topological orders (without symmetry). We find
explicit realizations for all the fermionic topological orders in the table.
For example, we find that, up to invertible
fermionic topological orders, there
are only four fermionic topological orders with one non-trivial topological
excitation: (1) the
fractional quantum Hall state, (2) a Fibonacci bosonic topological order
stacking with a fermionic product state, (3) the time-reversal
conjugate of the previous one, (4) a primitive fermionic topological order that
has a chiral central charge , whose only topological excitation has
a non-abelian statistics with a spin and a quantum dimension
. We also proposed a categorical way to classify 2+1D invertible
fermionic topological orders using modular extensions.Comment: 23 pages, 8 table
Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
We introduce the notion of algebraic higher symmetry, which generalizes
higher symmetry and is beyond higher group. We show that an algebraic higher
symmetry in a bosonic system in -dimensional space is characterized and
classified by a local fusion -category. We find another way to describe
algebraic higher symmetry by restricting to symmetric sub Hilbert space where
symmetry transformations all become trivial. In this case, algebraic higher
symmetry can be fully characterized by a non-invertible gravitational anomaly
(i.e. an topological order in one higher dimension). Thus we also refer to
non-invertible gravitational anomaly as categorical symmetry to stress its
connection to symmetry. This provides a holographic and entanglement view of
symmetries. For a system with a categorical symmetry, its gapped state must
spontaneously break part (not all) of the symmetry, and the state with the full
symmetry must be gapless. Using such a holographic point of view, we obtain (1)
the gauging of the algebraic higher symmetry; (2) the classification of
anomalies for an algebraic higher symmetry; (3) the equivalence between classes
of systems, with different (potentially anomalous) algebraic higher symmetries
or different sets of low energy excitations, as long as they have the same
categorical symmetry; (4) the classification of gapped liquid phases for
bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of
a topological order in one higher dimension (that corresponds to the
categorical symmetry). This classification includes symmetry protected trivial
(SPT) orders and symmetry enriched topological (SET) orders with an algebraic
higher symmetry.Comment: 61 pages, 31 figure
TFAD: A Decomposition Time Series Anomaly Detection Architecture with Time-Frequency Analysis
Time series anomaly detection is a challenging problem due to the complex
temporal dependencies and the limited label data. Although some algorithms
including both traditional and deep models have been proposed, most of them
mainly focus on time-domain modeling, and do not fully utilize the information
in the frequency domain of the time series data. In this paper, we propose a
Time-Frequency analysis based time series Anomaly Detection model, or TFAD for
short, to exploit both time and frequency domains for performance improvement.
Besides, we incorporate time series decomposition and data augmentation
mechanisms in the designed time-frequency architecture to further boost the
abilities of performance and interpretability. Empirical studies on widely used
benchmark datasets show that our approach obtains state-of-the-art performance
in univariate and multivariate time series anomaly detection tasks. Code is
provided at https://github.com/DAMO-DI-ML/CIKM22-TFAD.Comment: Accepted by the ACM International Conference on Information and
Knowledge Management (CIKM 2022
DCdetector: Dual Attention Contrastive Representation Learning for Time Series Anomaly Detection
Time series anomaly detection is critical for a wide range of applications.
It aims to identify deviant samples from the normal sample distribution in time
series. The most fundamental challenge for this task is to learn a
representation map that enables effective discrimination of anomalies.
Reconstruction-based methods still dominate, but the representation learning
with anomalies might hurt the performance with its large abnormal loss. On the
other hand, contrastive learning aims to find a representation that can clearly
distinguish any instance from the others, which can bring a more natural and
promising representation for time series anomaly detection. In this paper, we
propose DCdetector, a multi-scale dual attention contrastive representation
learning model. DCdetector utilizes a novel dual attention asymmetric design to
create the permutated environment and pure contrastive loss to guide the
learning process, thus learning a permutation invariant representation with
superior discrimination abilities. Extensive experiments show that DCdetector
achieves state-of-the-art results on multiple time series anomaly detection
benchmark datasets. Code is publicly available at
https://github.com/DAMO-DI-ML/KDD2023-DCdetector
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