  Isotropic but otherwise largely arbitrary Heisenberg models in the presence
of a homogeneous magnetic field are considered, including various integrable,
non-integrable, as well as disordered examples, and not necessarily restricted
to one dimension or short-range interactions. Taking for granted that the
non-equilibrium initial condition and the spectrum of the field-free model
satisfy some very weak requirements, expectation values of generic observables
are analytically shown to exhibit permanent long-time oscillations, thus ruling
out equilibration. If the model (but not necessarily the initial condition) is
translationally invariant, the long-time oscillations are moreover shown to
exhibit synchronization in the long run, meaning that they are invariant under
arbitrary translations of the observable. Analogous long-time oscillations are
also recovered for temporal correlation functions when the system is already at
thermal equilibrium from the outset, thus realizing a so-called time crystal.
