3,145 research outputs found
Microscopic Realization of 2-Dimensional Bosonic Topological Insulators
It is well known that a Bosonic Mott insulator can be realized by condensing
vortices of a bo- son condensate. Usually, a vortex becomes an anti-vortex (and
vice-versa) under time reversal symmetry, and the condensation of vortices
results in a trivial Mott insulator. However, if each vortex or anti-vortex
interacts with a spin trapped at its core, the time reversal transformation of
the composite vortex operator will contain an extra minus sign. It turns out
that such a composite vortex condensed state is a bosonic topological insulator
(BTI) with gapless boundary excitations protected by
symmetry. We point out that in BTI, an external flux monodromy defect
carries a Kramers doublet. We propose lattice model Hamiltonians to realize the
BTI phase, which might be implemented in cold atom systems or spin-1 solid
state systems.Comment: 5 pages + supplementary materia
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
Study on E- Business Platform of Electric Enterprise Group Based on the Perspective of System Synergy
the paper showcase the synergistic effect framework and apply it to a study on electricity energy groups of internet bidding platform on B2B supply business. We enumerate electricity grid enterprise group’s purchase system. Since 2006, by setting up the multi-layer purchase system based on internet. Chinese energy enterprise group began to adopt internet supply platform and take full advantage of synergistic effect and scale effects, decrease the trade cost of whole supply chain. From the perspective of system synergy, the paper firstly analyzed the model building on e-procurement platform, and then offered a set of evaluation index on synergistic effect, lastly through empirical analysis, point out there is not only positive synergistic effect but also negative synergistic effect on the e-business platform of the purchase system
New gapped quantum phases for S=1 spin chain with D2h symmetry
We study different quantum phases in integer spin systems with on-site
D2h=D2xZ2 and translation symmetry. We find four distinct non-trivial phases in
S=1 spin chains despite they all have the same symmetry. All the four phases
have gapped bulk excitations, doubly-degenerate end states and the
doubly-degenerate entanglement spectrum. These non-trivial phases are examples
of symmetry protected topological (SPT) phases introduced by Gu and Wen. One of
the SPT phase correspond to the Haldane phase and the other three are new.
These four SPT phases can be distinguished experimentally by their different
response of the end states to weak external magnetic fields. According to
Chen-Gu-Wen classification, the D2h symmetric spin chain can have totally 64
SPT phases that do not break any symmetry. Here we constructed seven nontrivial
phases from the seven classes of nontrivial projective representations of D2h
group. Four of these are found in S=1 spin chains and studied in this paper,
and the other three may be realized in S=1 spin ladders or S=2 models.Comment: 15+ pages,5 figures, 9 table
Symmetry protected Spin Quantum Hall phases in 2-Dimensions
Symmetry protected topological (SPT) states are short-range entangled states
with symmetry. Nontrivial SPT states have symmetry protected gapless edge
excitations. In 2-dimension (2D), there are infinite number of nontrivial SPT
phases with SU(2) or SO(3) symmetry. These phases can be described by
SU(2)/SO(3) nonlinear-sigma models with a quantized topological \theta-term. At
open boundary, the \theta-term becomes the Wess-Zumino-Witten term and
consequently the boundary excitations are decoupled gapless left movers and
right movers. Only the left movers (if \theta>0) carry the SU(2)/SO(3) quantum
numbers. As a result, the SU(2) SPT phases have a half-integer quantized spin
Hall conductance and the SO(3) SPT phases an even-integer quantized spin Hall
conductance. Both the SU(2)/SO(3) SPT phases are symmetric under their U(1)
subgroup and can be viewed as U(1) SPT phases with even-integer quantized Hall
conductance.Comment: 5 pages + appendi
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