6,748 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
Introduction to the Special Issue: Genome-Wide Association Studies
Introduction to the Special Issue: Genome-Wide Association StudiesComment: Published in at http://dx.doi.org/10.1214/09-STS310 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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
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