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Gapped Z_2 spin liquids have been proposed as candidates for the ground-stateof the S=1/2 quantum antiferromagnet on the Kagome lattice. We extend the useof Projected Entangled Pair States to construct (on the cylinder)ResonatingValence Bond (RVB) states including both nearest-neighbor and next-nearestneighbor singlet bonds. Our ansatz -- dubbed "simplex spin liquid" -- allowsfor an asymmetry between the two types of triangles (of order 2-3% in theenergy density after optimization) leading to the breaking of inversionsymmetry. We show that the topological Z_2 structure is still preserved and, byconsidering the presence or the absence of spinon and vison lines along aninfinite cylinder, we explicitly construct four orthogonal RVB MinimallyEntangled States. The spinon and vison coherence lengths are extracted from afinite size scaling w.r.t the cylinder perimeter of the energy splittings ofthe four sectors and are found to be of the order of the lattice spacing. Theentanglement spectrum of a partitioned (infinite) cylinder is found to begapless suggesting the occurrence, on a cylinder with {\it real} openboundaries, of gapless edge modes formally similar to Luttinger liquid(non-chiral) spin and charge modes. When inversion symmetry is spontaneouslybroken, the RVB spin liquid exhibits an extra Ising degeneracy, which mighthave been observed in recent exact diagonalisation studies.

physical review. b, condensed matter and materials physics

Simplex Z_2 spin liquids on the Kagome lattice with Entangled Pair  States: spinon and vison coherence lengths, topological entropy and gapless  edge modes