Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
Name
Ye-2013-Projective construction of two-dimensional.pdf
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Author(s)
Ye, Peng
Wen, Xiao-Gang
Date Issued
May 2013
Journal
Physical Review B
Publisher
American Physical Society
Citation
Ye, Peng, and Xiao-Gang Wen. “Projective Construction of Two-Dimensional Symmetry-Protected Topological Phases with U(1), SO(3), or SU(2) Symmetries.” Phys. Rev. B 87, no. 19 (May 2013). © 2013 American Physical Society
Version
Final published version
Abstract
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 Sz 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.87.195128
