  Resonating valence bond (RVB) states are of crucial importance in our
intuitive understanding of quantum spin liquids in 2D. We systematically
classify short-range bosonic RVB states into symmetric or nematic spin liquids
by examining their flux patterns. We further map short-range bosonic RVB states
into projected BCS wave functions, on which we perform large-scale Monte Carlo
simulations without the minus sign problem. Our results clearly show that both
spin and dimer correlations decay exponentially in all the short-range
frustrated (non-bipartite or $Z_2$) bosonic RVB states we studied, indicating
that they are gapped $Z_2$ quantum spin liquids. Generically, we conjecture
that all short-range frustrated bosonic RVB states in 2D have only short-range
correlations.
