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

Abstract: 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.