Fig. 1: Higher-order and fractional discrete time crystals.

a A spin-1/2 chain with long-range interactions and initial z-polarization is driven with a monochromatic transverse magnetic field of strength h, inducing a spin precession around x. b The time crystallinity is probed by the Fourier transform \(| \tilde{m}(\nu )|\) of the magnetization along z. The spectrum fragments in a multitude of plateaus with constant frequency 1/n for a magnetic field strength h in a finite range ≈1/n, each of which signals a higher-order n-DTC robust to perturbations of the drive (n is indicated in blue font for some of the resolved DTCs). Especially remarkable are fractional n-DTCs, with n = p/q and p and q some coprime integers. This spectrum refers to the LMG limit (α = 0, λ = 0), at fixed interaction J = 0.5, restricting to the first frequency Brillouin zone −0.5 ≤ ν ≤ 0.5, for 500 and 2000 drive periods in the top and bottom panels, respectively.