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A cornerstone assumption that most literature on discrete time crystals hasrelied on is that homogeneous Floquet systems generally heat to a featurelessinfinite temperature state, an expectation that motivated researchers in thefield to mostly focus on many-body localized systems. Some works have howevershown that the standard diagnostics for time crystallinity apply equally wellto clean settings without disorder. This fact raises the question whether anhomogeneous discrete time crystal is possible in which the originally expectedheating is evaded. Studying both a localized and an homogeneous model withshort-range interactions, we clarify this issue showing explicitly the keydifferences between the two cases. On the one hand, our careful scalinganalysis confirms that, in the thermodynamic limit and in contrast to localizeddiscrete time crystals, homogeneous systems indeed heat. On the other hand, weshow that, thanks to a mechanism reminiscent of quantum scars, finite-sizehomogeneous systems can still exhibit very crisp signatures of timecrystallinity. A subharmonic response can in fact persist over timescales thatare much larger than those set by the integrability-breaking terms, withthermalization possibly occurring only at very large system sizes (e.g., ofhundreds of spins). Beyond clarifying the emergence of heating in disorder-freesystems, our work casts a spotlight on finite-size homogeneous systems as primecandidates for the experimental implementation of nontrivial out-of-equilibriumphysics.

To heat or not to heat: time crystallinity and finite-size effects in clean Floquet systems