5,061 research outputs found
Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
We propose a general approach to construct symmetry protected topological
(SPT) states i.e the short-range entangled states with symmetry) in 2D
spin/boson systems on lattice. In our approach, we fractionalize spins/bosons
into different fermions, which occupy nontrivial Chern bands. After the
Gutzwiller projection of the free fermion state obtained by filling the Chern
bands, we can obtain SPT states on lattice. In particular, we constructed a
U(1) SPT state of a spin-1 model, a SO(3) SPT state of a boson system with
spin-1 bosons and spinless bosons, and a SU(2) SPT state of a spin-1/2 boson
system. By applying the "spin gauge field" which directly couples to the spin
density and spin current of components, we also calculate the quantum
spin Hall conductance in each SPT state. The projective ground states can be
further studied numerically in the future by variational Monte Carlo etc.Comment: 7+ pages, accepted by Phys. Rev.
Translation invariant topological superconductors on lattice
In this paper we introduce four Z_2 topological indices zeta_k=0,1 at
k=(0,0), (0,pi), (pi, 0), (pi, pi) characterizing 16 universal classes of 2D
superconducting states that have translation symmetry but may break any other
symmetries. The 16 classes of superconducting states are distinguished by their
even/odd numbers of fermions on even-by-even, even-by-odd, odd-by-even, and
odd-by-odd lattices. As a result, the 16 classes topological superconducting
states exist even for interacting systems. For non-interacting systems, we find
that zeta_k is the number of electrons on k=(0,0), (0,pi), (pi, 0), or (pi,pi)
orbitals (mod 2) in the ground state. For 3D superconducting states with only
translation symmetry, there are 256 different types of topological
superconductors.Comment: 4 pages, RevTeX
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