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