Resonating valence bond states in an electron-phonon system

We study a simple electron-phonon model that describes the effects of the vibration of bond atoms, through an asymptotically exact strong coupling analysis. When the electron-phonon coupling strength exceeds the charge transfer gap between the bond and the site orbitals and in a range of phonon retardation, we controllably obtain the Rokhsar-Kivelson quantum dimer model as the low-energy effective Hamiltonian at the density one electron per site. As varying phonon retardation, on the square lattice, there is a transition between distinct valence bond solids, separated by a solvable quantum critical line characterized by a resonating valence bond state. On the triangular lattice, a stable spin liquid phase occurs with Z2 topological order.