  We demonstrate analytically and numerically that the paradigmatic model of
quantum magnetism, the Heisenberg XXZ spin chain, does not relax to
stationarity and hence constitutes a genuine time crystal that does not rely on
external driving or coupling to an environment. We trace this phenomenon to the
existence of extensive dynamical symmetries and find their frequency to be a
no-where continuous (fractal) function of the anisotropy parameter of the
chain. We discuss how the ensuing persistent oscillations that violate one of
the most fundamental laws of physics could be observed experimentally and
identify potential metrological applications.
