Permanent oscillations and solitary wave behavior in flatband Heisenberg quantum spin systems

Research on the emergence of thermodynamics in closed quantum systems under unitary time evolution arrived at the consensus that generic systems equilibrate under rather general assumptions. A new focus of the field is thus on exceptions. Persistent oscillations are one possible hallmark of nonergodic time evolution. While time-crystalline behavior results from, e.g., many-body localization, here we show that ever-revolving solitary waves emerge in flatband Heisenberg quantum spin systems. This phenomenon is rather general for a variety of frustrated spin systems in one, two, and three dimensions as well as for Hubbard systems.