Charge density wave and quantum fluctuations in a molecular crystal

We consider an electron-phonon system in two and three dimensions on square, hexagonal and cubic lattices. The model is a modification of the standard Holstein model where the optical branch is appropriately curved in order to have a reflection positive Hamiltonian. Using infrared bounds together with a recent result on the coexistence of long-range order for electron and phonon fields, we prove that, at sufficiently low temperatures and sufficiently strong electron-phonon coupling, there is a Peierls instability towards a period two charge-density wave at half-filling. Our results take into account the quantum fluctuations of the elastic field in a rigorous way and are therefore independent of any adiabatic approximation. The strong coupling and low temperature regime found here is independent of the strength of the quantum fluctuations of the elastic field.