Thermodynamic saturation of the scarred discrete time-crystal lifetime

Determine whether the scarred discrete time-crystal lifetime saturates at a finite value beyond a critical system size because hybridization between approximate Floquet scar states and the thermal continuum eventually destroys the dynamical protection, rather than diverging with system size.

Background

The periodically driven dimerized spin chain exhibits long-lived period-doubled oscillations associated with approximate quantum many-body scars. Exact-diagonalization results show that the discrete time-crystal lifetime increases with system size over the accessible range, while the bulk Floquet spectrum simultaneously flows toward Wigner–Dyson statistics.

Because the scarred states are approximate rather than exact, they can hybridize with the exponentially dense thermal continuum as the system size grows. The paper therefore leaves unresolved whether the observed lifetime growth ultimately crosses over to saturation at a finite critical size, which would establish the SDTC as a metastable regime rather than a strictly stable thermodynamic phase.

References

We therefore expect $\tau_{\text{DTC}$ to saturate rather than diverge with $L$: by analogy with other approximate-scar models, the protection is eventually overcome by the scar--continuum hybridization, whose strength grows with the exponentially increasing density of states. The resulting saturation at a critical size $L_c$ ($\tau_{\text{DTC} \to \tau_{\text{sat}$ for $L \ge L_c$), lying beyond our current numerical reach, marks the observed SDTC as a long-lived metastable (prethermal) regime rather than a strictly stable thermodynamic phase.

— Scarred discrete time crystal in a periodically driven dimerized spin chain  (2608.16616 - Marripour et al., 17 Aug 2026) in Section 4, “The scarred discrete time crystalline (SDTC) phase,” paragraph beginning “We therefore expect”