19,646 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
Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
Bosonic topological insulators (BTI) in three dimensions are
symmetry-protected topological phases (SPT) protected by time-reversal and
boson number conservation {symmetries}. BTI in three dimensions were first
proposed and classified by the group cohomology theory which suggests two
distinct root states, each carrying a index. Soon after, surface
anomalous topological orders were proposed to identify different root states of
BTI, which even leads to a new BTI root state beyond the group cohomology
classification. In this paper, we propose a universal physical mechanism via
\textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three}
root states. It naturally produces bulk topological quantum field theory (TQFT)
description for each root state. Topologically ordered states on the surface
are \textit{rigorously} derived by placing TQFT on an open manifold, which
allows us to explicitly demonstrate the bulk-boundary correspondence. Finally,
we generalize the mechanism to symmetries and discuss potential SPT
phases beyond the group cohomology classification.Comment: ReVTeX 4.1 (published version
A universal form for quark and neutrino mass matrices
We propose a universal form for quark and lepton mass matrices, which applies
in a ``leading order'' approximation where -violating phases are ignored.
Down-quark mass ratios are successfully predicted in our scheme using the
measured CKM mixing angles as input. Assuming an additional discrete symmetry
in the neutrino sector, we obtain the ``golden ratio'' pattern in the
leading-order PMNS mixing matrix; in addition we predict an inverted neutrino
mass hierarchy with , , and
neutrinoless double beta decay mass parameter . We also predict that the -violating angle in the neutrino sector is
close to the maximal value , and that the diagonal phases in
the PMNS matrix are , .Comment: 4.5 pages, 2 figures, added references, added more discussions for
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