  We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated
square lattice. The diamond-like-decorated square lattice is a lattice in which
the bonds in a square lattice are replaced with diamond units. The diamond unit
has two types of antiferromagnetic exchange interactions, and the ratio
$\lambda$ of the diagonal bond strength to that of the other four edges
controls the frustration strength. For $0.974<\lambda<2$, the present system
has a nontrivial macroscopic degeneracy, which is called the macroscopically
degenerated tetramer-dimer (MDTD) states. The MDTD states are identical to the
Hilbert space of the Rokhsar-Kivelson (RK) quantum dimer model (QDM). By
introducing further neighbor couplings in the MDTD states, we calculate the
second-order effective Hamiltonian, which is exactly the same as the
square-lattice QDM with a finite hopping amplitude $t$ and dimer-dimer
interaction $v$. Furthermore, we calculate $v/|t|$ as a function of the ratio
$\lambda$ in the Heisenberg model and examine which phases of the
square-lattice QDM appear in our obtained states. Our obtained QDM has a region
where $\lambda$ exhibits a finite hopping amplitude ($|t|>0$) and repulsive
interaction between dimers ($v>0$). This suggests the possibility of realizing
the resonating valence bond (RVB) state because the RVB state is obtained at
$v=|t|$, which is known as the RK point.
