  We construct a short-range resonating valence-bond state (RVB) on the ruby
lattice, using projected entangled-pair states (PEPS) with bond dimension
$D=3$. By introducing non-local moves to the dimer patterns on the torus, we
distinguish four distinct sectors in the space of dimer coverings, which is a
signature of the topological nature of the RVB wave function. Furthermore, by
calculating the reduced density matrix of a bipartition of the RVB state on an
infinite cylinder and exploring its entanglement entropy, we confirm the
topological nature of the RVB wave function by obtaining non-zero topological
contribution, $\gamma=-\rm{ln}\ 2$, consistent with that of a $\mathbb{Z}_2$
topological quantum spin liquid. We also calculate the ground-state energy of
the spin-$\frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice
and compare it with the RVB energy. Finally, we construct a quantum-dimer model
for the ruby lattice and discuss it as a possible parent Hamiltonian for the
RVB wave function.

Strongly Correlated Electrons;Quantum Physics