1,522 research outputs found
Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
Classification and construction of symmetry protected topological (SPT)
phases in interacting boson and fermion systems have become a fascinating
theoretical direction in recent years. It has been shown that the (generalized)
group cohomology theory or cobordism theory can give rise to a complete
classification of SPT phases in interacting boson/spin systems. Nevertheless,
the construction and classification of SPT phases in interacting fermion
systems are much more complicated, especially in 3D. In this work, we revisit
this problem based on the equivalent class of fermionic symmetric local unitary
(FSLU) transformations. We construct very general fixed point SPT wavefunctions
for interacting fermion systems. We naturally reproduce the partial
classifications given by special group super-cohomology theory, and we show
that with an additional (the so-called
obstruction free subgroup of ) structure, a complete
classification of SPT phases for three-dimensional interacting fermion systems
with a total symmetry group can be obtained for
unitary symmetry group . We also discuss the procedure of deriving a
general group super-cohomology theory in arbitrary dimensions.Comment: 48 pages, 35 figures, published versio
Historical Development of the Undergraduate Educational Model at BIT from the Perspective of Suzhi Education
From the perspective of suzhi education, this study analyses the historical development of the undergraduate educational model at Beijing Institute of Technology (BIT). It could be argued that BIT’s talent-cultivating system’s transformations from 1940 to 2020 echo Chinese higher education’s reform and development. This study concludes that BIT has experienced four phases: (1) from advocacy for general-specialized education’s integration to general education’s disappearance, (2) from the rectification of specialized education to the germination of suzhi and general education, (3) the flourishing of suzhi education and general education, and (4) the establishment of the Shuyuan System. The case of BIT reflects Chinese higher education’s development and the process of transforming from meritocracy to popularization. Chinese universities have changed their paradigm from emphasizing specialized education to highlighting suzhi education, as well as from focusing on training students into specialists to stressing students’ holistic development
Para-fusion Category and Topological Defect Lines in -parafermionic CFTs
We study topological defect lines (TDLs) in two-dimensional -parafermoinic CFTs. Different from the bosonic case, in the 2d
parafermionic CFTs, there exist parafermionic defect operators that can live on
the TDLs and satisfy interesting fractional statistics. We propose a
categorical description for these TDLs, dubbed as ``para-fusion category",
which contains various novel features, including -type objects
for , and parafermoinic defect operators as a type of specialized
1-morphisms of the TDLs. The para-fusion category in parafermionic CFTs can be
regarded as a natural generalization of the super-fusion category for the
description of TDLs in 2d fermionic CFTs. We investigate these distinguishing
features in para-fusion category from both a 2d pure CFT perspective, and also
a 3d anyon condensation viewpoint. In the latter approach, we introduce a
generalized parafermionic anyon condensation, and use it to establish a functor
from the parent fusion category for TDLs in bosonic CFTs to the para-fusion
category for TDLs in the parafermionized ones. At last, we provide many
examples to illustrate the properties of the proposed para-fusion category, and
also give a full classification for a universal para-fusion category obtained
from parafermionic condensation of Tambara-Yamagami fusion
category.Comment: 45+4 page
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