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arXiv:2609.33574

Interactions Protect Periodically Driven Time Crystals Against Dephasing but Destabilise Multipolar-Driven Order

Karthikeya Machiraju, Kaustav Bhowmick

quant-phcond-mat.dis-nnSubmitted Sep 27, 2026• Announced Sep 29, 2026• 0 citations
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Abstract

We show that stronger interactions protect periodically driven time-crystal order against dephasing but destabilise order under random multipolar drives, and that coordination matters beyond the total interaction strength. We studied a disordered kicked Ising model of $N=12$ and $16$ spins with imperfect $π$ pulses and per-site dephasing by exact diagonalisation, comparing a periodic drive, random multipolar drives of order $n=0,1,2$ and the Thue-Morse sequence, and separated coupling strength from coordination by comparing a grid with a ring at equal total interaction strength $zJ$. For the periodic drive the coherence time scales approximately as $1/γ$, and stronger coupling reduces the transverse tilt on which dephasing acts. For multipolar drives of order $n\ge1$, doubling the coupling on a ring shortens the coherence time to $0.54$ ($n=1$), $0.37$ ($n=2$) and $0.44$ (Thue-Morse) at $N=16$, while random signs ($n=0$) are unaffected. A disorder scan supports a toggling-frame picture in which interactions spoil the block cancellation of the pulse error. At equal $zJ$ the grid outlives the ring by $2.15$ ($N=12$) and $2.78$ ($N=16$) for the periodic drive despite an identical transverse tilt, a coordination effect beyond this picture. All ratios hold under three definitions of the coherence time.

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We show that stronger interactions protect periodically driven time-crystal order against dephasing but destabilise order under random multipolar drives, and that coordination matters beyond the total interaction strength. We studied a disordered kicked Ising model of N=12N=12N=12 and 161616 spins with imperfect πππ pulses and per-site dephasing by exact diagonalisation, comparing a periodic drive, random multipolar drives of order n=0,1,2n=0,1,2n=0,1,2 and the Thue-Morse sequence, and separated coupling strength from coordination by comparing a grid with a ring at equal total interaction strength zJzJzJ. For the periodic drive the coherence time scales approximately as 1/γ1/γ1/γ, and stronger coupling reduces the transverse tilt on which dephasing acts. For multipolar drives of order n≥1n\ge1n≥1, doubling the coupling on a ring shortens the coherence time to 0.540.540.54 (n=1n=1n=1), 0.370.370.37 (n=2n=2n=2) and 0.440.440.44 (Thue-Morse) at N=16N=16N=16, while random signs (n=0n=0n=0) are unaffected. A disorder scan supports a toggling-frame picture in which interactions spoil the block cancellation of the pulse error. At equal zJzJzJ the grid outlives the ring by 2.152.152.15 (N=12N=12N=12) and 2.782.782.78 (N=16N=16N=16) for the periodic drive despite an identical transverse tilt, a coordination effect beyond this picture. All ratios hold under three definitions of the coherence time.
Discrete time crystals (DTC) have emerged as a significant phase of matter for out-of-equilibrium many-body systems. In this work, we study how random long-range interactions contribute to the stability of the DTC phase. Generally, a stable DTC phase is believed to be realized in disordered systems with short-range interactions. Here, we explore a periodically driven quantum Sherrington-Kirkpatrick (SK) model of Ising spin-glass in which all spins are coupled to each other randomly. We investigate the possibilities of the DTC phase in the SK model within three different driving protocols and found that the quantum SK model exhibits a robust DTC phase, although systems with uniform long-range interactions can exhibit only prethermal DTC phase. Further, we demonstrate that disorder in the local XYXYXY term or transverse field is crucial for stabilizing a broad DTC phase, despite random couplings in the SK model. Our analysis shows that the stability of the DTC phase is determined by the non-ergodic nature of the Floquet eigenstates.
A discrete time is a remarkable non-equilibrium phase of matter characterized by persistent sub-harmonic response to a periodic drive. Motivated by the question of whether such time-crystalline order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasiperiodic kicking. Intriguingly, this infinite-range-interacting spin chain can exhibit long-lived periodic oscillations when the kicking amplitudes are drawn from the Thue-Morse sequence (TMS). We dub this phase a ``self-ordered time crystal (SOTC), and demonstrate that our model hosts at least two qualitatively distinct prethermal SOTC phases. These SOTCs are robust to various perturbations, and they originate from the interplay of long-range interactions and the recursive structure of the TMS. Our results suggest that quasiperiodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.
We study the unitary dynamics of randomly or quasiperiodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase starting from a Z2{\mathbb{Z}}_{2}Z2​ symmetry-broken state. The randomness is implemented via a telegraph noise protocol in the drive period while the quasiperiodic drive is chosen to correspond to a Thue-Morse sequence. The periodically driven tBH model (with a square pulse protocol characterized by a time period TTT) is known to exhibit transitions from dynamical regimes with long-time coherent oscillations to those with rapid thermalization. Here we show that starting from a regime where the periodic drive leads to rapid thermalization, a random drive, which consists of a random sequence of square pulses with period $T+\ensuremath{\alpha}dT$, where $\ensuremath{\alpha}=\ifmmode\pm\else\textpm\fi{}1$ is a random number and dTdTdT is the amplitude of the noise, restores long-time coherent oscillations for special values of dTdTdT. A similar phenomenon can be seen for a quasiperiodic drive following a Thue-Morse sequence where such coherent behavior is shown to occur for a larger number of points in the (T,dT)(T,dT)(T,dT) plane due to the additional structure of the drive protocol. We chart out the dynamics of the system in the presence of such aperiodic drives, provide a qualitative analytical understanding of this phenomenon, point out the role of quantum scars behind it, and discuss experiments which can test our theory.
Discrete time crystals are periodically driven systems characterized by a response with periodicity nT, with T the period of the drive and n > 1. Typically, n is an integer and bounded from above by the dimension of the local (or single particle) Hilbert space, the most prominent example being spin-1/2 systems with n restricted to 2. Here, we show that a clean spin-1/2 system in the presence of long-range interactions and transverse field can sustain a huge variety of different 'higher-order' discrete time crystals with integer and, surprisingly, even fractional n > 2. We characterize these (arguably prethermal) non-equilibrium phases of matter thoroughly using a combination of exact diagonalization, semiclassical methods, and spin-wave approximations, which enable us to establish their stability in the presence of competing long- and short-range interactions. Remarkably, these phases emerge in a model with continous driving and time-independent interactions, convenient for experimental implementations with ultracold atoms or trapped ions.
A discrete time crystal (DTC) is a remarkable non-equilibrium phase of matter characterized by the persistent sub-harmonic oscillations of physical observables in periodically driven many-body systems. Motivated by the question of whether such a temporal periodic order can persist when the drive becomes aperiodic, we investigate the dynamics of a Lipkin-Meshkov-Glick model under quasi-periodic Thue-Morse (TM) driving. Intriguingly, this infinite-range-interacting spin system can host "quasi-discrete time crystal" (quasi-DTC) phases characterized by periodic oscillations of the magnetization. We demonstrate that our model can host the quasi-DTC analog of both period-doubling DTCs as well as higher-order DTCs. These quasi-DTCs are robust to various perturbations, and they originate from the interplay of "all-to-all" interactions and the recursive structure of the TM sequence. Our results suggest that quasi-periodic driving protocols can provide a promising route for realizing novel non-equilibrium phases of matter in long-range interacting systems.
A discrete time crystal is a recently discovered nonequilibrium phase of matter that has been shown to exist in disordered, periodically driven Ising spin chains. In this phase, if the system is initially prepared in one of a certain class of pure multispin product states, it periodically returns to this state over very long timescales despite the presence of interactions, disorder, and pulse imperfections. Here, we show that this phase occurs in GaAs quantum dot spin arrays containing as few as three quantum dots, each confining one electron spin, for naturally occurring levels of nuclear spin noise and charge noise. Although the physical interaction in these arrays is a nearest-neighbor Heisenberg exchange interaction, we show that this can be effectively converted into an Ising interaction by applying additional pulses during each drive period. We show that by changing the rotation axis of these pulses, we can select the direction of the Ising interaction and, consequently, the quantization axis of the stabilized multispin states. Moreover, we demonstrate that it is possible to perform coherent rotations of the stabilized states while remaining in the time-crystal phase. These findings open up the intriguing possibility of using time-crystal phases to extend the lifetime of quantum states for information applications.