  We consider a hybrid quantum many-body system formed by both a vibrational
mode of a nanomembrane, which interacts optomechanically with light in a
cavity, and an ultracold atom gas in the optical lattice of the out-coupled
light. After integrating over the light field, an effective Hamiltonian reveals
a competition between the localizing potential force and the membrane
displacement force. For increasing atom-membrane interaction we find a
nonequilibrium quantum phase transition from a localized non-motional phase of
the atom cloud to a phase of collective motion. Near the quantum critical
point, the energy of the lowest collective excitation vanishes, while the order
parameter of the condensate becomes non-zero in the symmetry-broken state. The
effect occurs when the atoms and the membrane are non-resonantly coupled.
