Didier Poilblanc, Norbert Schuch
Gapped Z_2 spin liquids have been proposed as candidates for the ground-state of the S=1/2 quantum antiferromagnet on the Kagome lattice. We extend the use of Projected Entangled Pair States to construct (on the cylinder)Resonating Valence Bond (RVB) states including both nearest-neighbor and next-nearest neighbor singlet bonds. Although, by construction, inversion symmetry is broken, after energy optimization the resulting asymmetry between the two types of triangles is only of order 2-3% in the energy density. By considering the presence or the absence of spinon and vison lines along an infinite cylinder, we explicitly construct four orthogonal RVB Minimally Entangled States. The spinon and vison coherence lengths are extracted from a finite size scaling w.r.t the cylinder perimeter of the energy splittings of the four sectors and are found to be of the order of the lattice spacing. The entanglement spectrum of a partitioned (infinite) cylinder is found to be gapless suggesting the occurrence of gapless edge modes on a cylinder with open boundaries protected by Z_2 topological invariants, translational invariance and SU(2) symmetry. When inversion symmetry is broken, the RVB spin liquid exhibits, in addition to its topological Z_2 structure, an extra Ising degeneracy, which might have been observed in recent exact diagonalisation studies.
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http://arxiv.org/abs/1302.0306
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