Local Dephasing Sustains Continuous Time Crystals in a Spin-1/2 Ensemble

Zhen-huan Yang; Dan-Bo Zhang

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arXiv · 2610.31230

Local Dephasing Sustains Continuous Time Crystals in a Spin-1/2 Ensemble

Zhen-huan Yang·Dan-Bo Zhang

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Abstract

Local pure dephasing suppresses single-spin coherence, yet we show that it sustains continuous time-crystalline order in a fully connected ferromagnetic spin-$1/2$ ensemble with local decay. An exact operator identity reveals the mechanism: dephasing raises the interaction energy, while energy relaxation on a finite timescale converts this charging into delayed feedback. Within homogeneous mean-field theory, we prove that dephasing is necessary for periodic motion in this model and that feedback exactly balances transverse damping over each cycle. Beyond mean field, the identity fixes the relative amplitude and phase of energy and longitudinal magnetization in oscillatory Liouvillian modes. Liouvillian spectra and stationary two-time correlations characterize temporal order through decay rates that decrease algebraically with system size, frequencies approaching nonzero mean-field values, and comparable per-spin oscillatory weights. Semiclassical trajectories further reveal recurrent switching between a limit-cycle region and two symmetry-related stationary regions: fluctuations interrupt and reactivate collective oscillations, and oscillatory episodes provide an intermediate channel between stationary regions. These results establish local dephasing as a resource for autonomous collective motion and show how the resulting temporal order can participate in metastable dynamics.

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Zhen-huan Yang, Dan-Bo Zhang. 2026-10-22. Local Dephasing Sustains Continuous Time Crystals in a Spin-1/2 Ensemble. https://arxiv.org/abs/2610.31230

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