  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.
