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.
Approach
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.
Main Findings
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.
Why It Matters
This work demonstrates that Floquet time crystals can emerge from the internal structure of quantum scars rather than requiring external disorder (like many-body localization). By showing that specific initial configurations can "tap into" these non-thermal scarred states, the authors provide a mechanism for realizing time-crystalline phases in clean, long-range interacting systems, bridging the gap between quantum scarring and non-equilibrium phase transitions.
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