Gapped Z_2 spin liquids have been proposed as candidates for the ground-state of the S=1/2 quantum antiferromagnet on frustrated lattices (like the Kagome lattice). We use Projected Entangled Pair States (PEPS) to construct (on the cylinder) Resonating Valence Bond (RVB) states. 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 then extracted from a finite size scaling w.r.t the cylinder perimeter of the energy splittings of the four sectors.
A large enough magnetic field can generically induce "doping" of polarized S=1/2 spinons. On the bipartite honeycomb lattice, simple PEPS can describe Bose condensed spinons (RVB) superfluids with transverse staggered (Néel) magnetic order. On the Kagome lattice, doping the RVB state with deconfined spinons or triplons (i.e. spinon bound pairs) yields uncondensed Bose liquids preserving U(1) spin-rotation symmetry.
Lastly, considering fermoionic PEPS, we construct doped fermionic RVB superconductors and investigate their properties and relevance to frustrated t-J models.
The entanglement spectra and hamiltonians of the corresponding PEPS on a partitioned (infinite) cylinder are also discussed.