Quantum dimer model containing Rokhsar-Kivelson point expressed by spin- 12 Heisenberg antiferromagnets

Abstract

We obtain a quantum dimer model (QDM) containing a Rokhsar-Kivelson (RK) point expressed by spin-$\frac{1}{2}$ Heisenberg antiferromagnets on a diamond-like decorated square lattice. This lattice has macroscopically degenerated nonmagnetic ground states, which are equivalent to the Hilbert space of a square-lattice QDM. Then, a square-lattice QDM containing the RK point as a second-order effective Hamiltonian is obtained by introducing further neighbor couplings as perturbation. Our model can provide a new method for the experimental realization of a resonating valence bond state in the QDM.