Discrete Time Crystal Order in Spin-Chains Enabled by Floquet Flat-Bands

TL;DR

This paper introduces a new method using Floquet flat-bands to realize stable discrete time-crystal order in clean spin chains, broadening the understanding of non-equilibrium phases without disorder.

Contribution

The authors propose a flat-band driven protocol to stabilize DTC order in clean spin chains, demonstrating broader parameter tunability compared to disorder-based methods.

Findings

Stable DTC observed with a clear subharmonic response.

Flat-band protocol offers greater tunability of drive parameters.

Sensitivity to spin-rotation errors can be mitigated with additional interactions.

Abstract

We propose a novel protocol to realize discrete time-crystal (DTC) order in clean, periodically driven spin-$1/2$ chains. In each drive cycle, a global spin flip is followed by a two-tone flat-band segment. This flat-band segment engineers a fully degenerate Floquet quasienergy spectrum, suppresses thermalization, and stabilizes a robust period-doubled subharmonic response. Using exact time evolution, we identify a pronounced subharmonic peak at half the drive frequency in the Fourier spectrum of the order parameter, thereby providing clear evidence for the emergence of stable DTC. The resulting phase is insensitive to system size, interaction strength, and interaction range; however, it remains sensitive to spin-rotation errors ($\varepsilon_r$), which can destabilize the subharmonic response. Compared with disorder-induced many-body localized (MBL) and disorder-free dynamically many-body localized (DMBL) DTCs, we find that the exact flat-band protocol offers a broader tunability of drive parameters, whereas MBL and DMBL based DTCs are more resistant to $\varepsilon_r$. In particular, the $\varepsilon_r$ sensitivity can be suppressed by incorporating additional spin-spin interactions that have modest deviations from the ideal flat-band protocol. This manifests itself in a robust DTC response over a finite window of spin-coupling strengths and drive frequencies. Our results establish flat-band driving as a versatile and experimentally relevant route to DTC order in disorder-free spin systems and motivate further exploration of non-equilibrium phases.