We study a short-range resonating valence bond (RVB) wave function with diagonal links on the square lattice that permits sign-problem free wave function Monte Carlo studies. Special attention is given to entanglement properties, in particular, the study of minimum entropy states (MES) according to the method of Zhang et al. [Phys. Rev. B 85, 235151 (2012)]. We provide evidence that the MES associated with the RVB wave functions can be lifted from an associated quantum dimer picture of these wave functions, where MES states are certain linear combinations of eigenstates of a 't Hooft ``magnetic loop''-type operator. From this identification, we calculate a value consistent with
ln(2) for the topological entanglement entropy directly for the RVB states via wave function Monte Carlo. This corroborates the
Z2 nature of the RVB states. We furthermore define and elaborate on the concept of a ``pre-Kasteleyn'' orientation that may be useful for the study of lattices with nonplanar topology in general.
We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the J_1-J_2 J 1 − J 2 frustrated Heisenberg model. For J_2/J_1\sim 0.55 J 2 / J 1 ∼ 0.55 we show the emergence of critical (algebraic) dimer-dimer correlations – typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices – while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.