9,535 research outputs found
Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
It has been shown that the symmetry-protected topological (SPT) phases with
finite Abelian symmetries can be described by Chern-Simons field theory. We
propose a topological response theory to uniquely identify the SPT orders,
which allows us to obtain a systematic scheme to classify bosonic SPT phases
with any finite Abelian symmetry group. We point out that even for finite
Abelian symmetry, there exist bosonic SPT phases beyond the current
Chern-Simons theory framework. We also apply the theory to fermionic SPT phases
with symmetry and find the classification of SPT phases depends
on the parity of : for even there are classes, out of which is
intrinsically fermionic SPT phases and can not be realized in any bosonic
system. Finally we propose a classification scheme of fermionic SPT phases for
any finite, Abelian symmetry.Comment: published versio
Classification of Symmetry-Protected Phases for Interacting Fermions in Two Dimensions
Recently, it has been shown that two-dimensional bosonic symmetry-protected
topological(SPT) phases with on-site unitary symmetry can be completely
classified by the group cohomology class . Later, group
super-cohomology class was proposed as a partial classification for SPT phases
of interacting fermions. In this work, we revisit this problem based on the
mathematical framework of -extension of unitary braided tensor
category(UBTC) theory. We first reproduce the partial classifications given by
group super-cohomology, then we show that with an additional structure, a complete classification of SPT phases for
two-dimensional interacting fermion systems for a total symmetry group
can be achieved. We also discuss the classification of
interacting fermionic SPT phases protected by time-reversal symmetry.Comment: references added; published versio
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