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We study spin-1/2 Heisenberg antiferromagnets on a diamond-like-decoratedsquare lattice. The diamond-like-decorated square lattice is a lattice in whichthe bonds in a square lattice are replaced with diamond units. The diamond unithas two types of antiferromagnetic exchange interactions, and the ratio$\lambda$ of the diagonal bond strength to that of the other four edgescontrols the frustration strength. For $0.974<\lambda<2$, the present systemhas a nontrivial macroscopic degeneracy, which is called the macroscopicallydegenerated tetramer-dimer (MDTD) states. The MDTD states are identical to theHilbert space of the Rokhsar-Kivelson (RK) quantum dimer model (QDM). Byintroducing further neighbor couplings in the MDTD states, we calculate thesecond-order effective Hamiltonian, which is exactly the same as thesquare-lattice QDM with a finite hopping amplitude $t$ and dimer-dimerinteraction $v$. Furthermore, we calculate $v/|t|$ as a function of the ratio$\lambda$ in the Heisenberg model and examine which phases of thesquare-lattice QDM appear in our obtained states. Our obtained QDM has a regionwhere $\lambda$ exhibits a finite hopping amplitude ($|t|>0$) and repulsiveinteraction between dimers ($v>0$). This suggests the possibility of realizingthe resonating valence bond (RVB) state because the RVB state is obtained at$v=|t|$, which is known as the RK point.

aip advances

Novel constructive method for the quantum dimer model in spin-1/2  Heisenberg antiferromagnets with frustration on a diamond-like-decorated  square lattice