  We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decorated
square lattice perturbed by two kinds of further neighbor couplings. In our
previous study [J. Phys. Soc. Jpn. 85, 094002 (2016)], the second-order
effective Hamiltonian for the Heisenberg model perturbed by a further neighbor
coupling was found to be a square-lattice quantum-dimer model with a finite
hopping amplitude, t>0, and no dimer-dimer interaction, v=0. In this study, we
introduce another kind of further neighbor coupling and show that it leads to
an attractive interaction between dimers, which suggests the stabilization of
the columnar phase of the square-lattice quantum-dimer model. The calculated
v/t is presented as a function of the ratio of the two exchange parameters in
the Heisenberg model.
