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arXiv · 2203.16562

Fractal nature of high-order time crystal phases

Guido Giachetti·Andrea Solfanelli·Lorenzo Correale·Nicolò Defenu
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Abstract

Discrete Floquet time crystals (DFTC) are characterized by the spontaneous breaking of the discrete time-translational invariance characteristic of Floquet driven systems. In analogy with equilibrium critical points, also time-crystalline phases display critical behaviour of different order, i.e., oscillations whose period is a multiple $p > 2$ of the Floquet driving period. Here, we introduce a new, experimentally-accessible, order parameter which is able to unambiguously detect crystalline phases regardless of the value of $p$ and, at the same time, is a useful tool for chaos diagnostic. This new paradigm allows us to investigate the phase diagram of the long-range (LR) kicked Ising model to an unprecedented depth, unveiling a rich landscape characterized by self-similar fractal boundaries. Our theoretical picture describes the emergence of DFTCs phase both as a function of the strength and period of the Floquet drive, capturing the emergent $\mathbb{Z}_p$ symmetry in the Floquet-Bloch waves.

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Guido Giachetti, Andrea Solfanelli, Lorenzo Correale, Nicolò Defenu. 2023-11-16. Fractal nature of high-order time crystal phases. https://doi.org/10.1103/physrevb.108.l140102

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