Quantum many-body scars leading to time-translation symmetry breaking in kicked interacting spin models

The authors investigate whether periodically kicked, long-range interacting Ising spin chains can exhibit Floquet time crystal behavior—specifically, persistent period-doubling oscillations—in the absence of disorder. The study focuses on whether this phenomenon arises from "quantum scars," which are a minority of non-thermal eigenstates embedded within a sea of thermal states.

The researchers analyze a 1D Ising model with power-law interactions subjected to periodic "kicks" (time-periodic driving). To identify time-translation symmetry breaking, they examine the properties of the system's Floquet eigenstates:

• $\pi$-spectral pairing: They identify doublets of Floquet states separated by a gap of $\pi/\tau$ (where $\tau$ is the driving period).
• Long-range order: They diagonalize the magnetization operator within these doublets to check for cat-state superpositions, which indicate long-range correlations.
• Overlap Analysis: They compare how different initial states (e.g., specific domain-wall configurations vs. tilted spin states) overlap with these "scarred" Floquet states to predict the longevity of period-doubling oscillations.

• Weak Ergodicity Breaking: The system exhibits a "scarring" phenomenon where only a minority of Floquet states are non-thermal. Despite being a minority, the number of these states grows exponentially with system size, making them physically relevant.
• Persistent Period Doubling: For initial states with significant overlap with these scarred doublets, the system displays robust period-doubling oscillations.
• Finite-Size Scaling: For tilted initial states, the $\pi$-shifted gap decreases exponentially with system size, suggesting that the period-doubling oscillations can persist for times that are also exponential in the system size.
• Robustness: This behavior persists even when the system is globally chaotic and the majority of the spectrum follows random-matrix theory predictions.