  A translation invariant system of interacting quantum anharmonic oscillators
indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered.
The anharmonic potential is of general type, which in particular means that it
might have no symmetry. For this system, we prove that the global polarization
(obtained in the thermodynamic limit) gets discontinuous at a certain value of
the external field provided $d\geq 3$, and the particle mass as well as the
interaction intensity are big enough. The proof is based on the representation
of local Gibbs states in terms of path measures and thereby on the use of the
infrared estimates and the Garsia-Rodemich-Rumsey inequality.
