Floquet Time Crystals (DTC) spontaneously break discrete time-translation symmetry.
Under periodic π-pulse driving H(t) = H₁ (0<t<T/2) + H₂ (T/2<t<T), spins oscillate at 2T period, not T.
MBL (many-body localization) from disorder h protects the phase against drive errors ε and interactions J.
Left: spin configuration over time. Right: order parameter |m(t)| showing period-2 oscillation.