We aim to describe the cluster states of nuclear systems starting with a realistic interaction, which is a challenge of modern nuclear theories. Here, the short-range correlation of realistic interaction is treated by employing the damping factor, and the resultant interaction can be applied to the cluster structure of light nuclei. We start with a realistic interaction (G3RS) and transform it in this way, and the $alpha$-$alpha$ energy curve is compared with the results of phenomenological interactions. The attractive effect between two $alpha$s is found to be not enough even with a damping factor for the short-range repulsion, and the necessity of a finite-range three-body term is discussed. With this three-body term, the resonance energy of the ground state and the scattering phase shift of two $alpha$s can be reproduced. Also, the binding energy of $^{16}$O from the four $alpha$ threshold is reasonably reproduced. The linear-chain structure of three and four $alpha$ clusters in $^{12}$C and $^{16}$O are calculated with this interaction and compared with the results of the conventional approaches including the density functional theories.
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