  The aim of this paper is to propose a criterion of spontaneous symmetry
breaking that makes reference to the properties of pure phases defined by a
translationally invariant state. By avoiding any reference to the ground state,
at the basis of the standard approach, this criterion applies to a wider class
of models. An interesting application is the breaking of time translations.
Indeed, we discuss explicit theoretical models which exhibit the prototypical
features of quantum time crystals, without the need of a time-dependent
Hamiltonian.
