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Symmetry protected topological orders and the group cohomology of their symmetry group
Symmetry protected topological (SPT) phases are gapped short-range-entangled
quantum phases with a symmetry G. They can all be smoothly connected to the
same trivial product state if we break the symmetry. The Haldane phase of
spin-1 chain is the first example of SPT phase which is protected by SO(3) spin
rotation symmetry. The topological insulator is another exam- ple of SPT phase
which is protected by U(1) and time reversal symmetries. It has been shown that
free fermion SPT phases can be systematically described by the K-theory. In
this paper, we show that interacting bosonic SPT phases can be systematically
described by group cohomology theory: distinct d-dimensional bosonic SPT phases
with on-site symmetry G (which may contain anti-unitary time reversal symmetry)
can be labeled by the elements in H^{1+d}[G, U_T(1)] - the Borel (1 +
d)-group-cohomology classes of G over the G-module U_T(1). The boundary
excitations of the non-trivial SPT phases are gapless or degenerate. Even more
generally, we find that the different bosonic symmetry breaking
short-range-entangled phases are labeled by the following three mathematical
objects: (G_H, G_{\Psi}, H^{1+d}[G_{\Psi}, U_T(1)], where G_H is the symmetry
group of the Hamiltonian and G_{\Psi} the symmetry group of the ground states.Comment: 55 pages, 42 figures, RevTeX4-1, included some new reference
Interchange reconnection associated with a confined filament eruption: Implications for the source of transient cold-dense plasma in solar winds
The cold-dense plasma is occasionally detected in the solar wind with in situ
data, but the source of the cold-dense plasma remains illusive. Interchange
reconnections (IRs) between closed fields and nearby open fields are well known
to contribute to the formation of solar winds. We present a confined filament
eruption associated with a puff-like coronal mass ejection (CME) on 2014
December 24. The filament underwent successive activations and finally erupted,
due to continuous magnetic flux cancellations and emergences. The confined
erupting filament showed a clear untwist motion, and most of the filament
material fell back. During the eruption, some tiny blobs escaped from the
confined filament body, along newly-formed open field lines rooted around the
south end of the filament, and some bright plasma flowed from the north end of
the filament to remote sites at nearby open fields. The newly-formed open field
lines shifted southward with multiple branches. The puff-like CME also showed
multiple bright fronts and a clear southward shift. All the results indicate an
intermittent IR existed between closed fields of the confined erupting filament
and nearby open fields, which released a portion of filament material (blobs)
to form the puff-like CME. We suggest that the IR provides a possible source of
cold-dense plasma in the solar wind
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