Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube.

@article{Lajk2012ExactGS,
  title={Exact ground states with deconfined gapless excitations for the three-leg spin-1/2 tube.},
  author={Mikl{\'o}s Lajk{\'o} and Philippe Sindzingre and K. Penc},
  journal={Physical review letters},
  year={2012},
  volume={108 1},
  pages={
          017205
        }
}
We consider a spin-1/2 tube (a three-leg ladder with periodic boundary conditions) with a Hamiltonian given by two projection operators-one on the triangles and the other on the square plaquettes on the side of the tube-that can be written in terms of Heisenberg and four-spin ring exchange interactions. We identify 3 phases: (i) for strongly antiferromagnetic exchange on the triangles, an exact ground state with a gapped spectrum can be given as an alternation of spin and chirality singlet… 
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