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arXiv:2507.15565

Discrete time crystal and perfect many-body tunneling in a periodically driven Heisenberg spin chain

Xiaotong Chen, Jianda Wu

Published Jul 21, 2025• 0 citations
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Abstract

We investigate the non-equilibrium dynamics of a Heisenberg spin-1/2 chain driven by a periodic magnetic field. Based on its instantaneous integrability and inherent symmetry, we analytically study the magnetization and many-body tunneling (MBT). Both of them exhibit periodicity distinct from the driving period. The magnetization is shown to be independent of the initial state and robust against perturbations, signaling the formation of discrete time crystal (DTC) order. The DTC phase is found to be continuously tunable through magnetic field. The system exhibits perfect MBT, manifested as exactly vanishing Loschmidt echo (LE) thus divergent LE rate function at half period of the DTC. Remarkably, the perfect MBT is independent of the system size, and can be traced to an effective gap closure induced by quantum geometric effects. Furthermore, the Loschmidt echo spectra entropy shows logarithmic-dependence on system size, consistent with non-thermal nature of the DTC phase. We propose a protocol using ultracold atoms for experimental realization of the DTC and MBT.

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Time crystal embodies chimeralike state in periodically driven quantum spin system

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Abstract Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to the complex interdependence between quantum entanglement and the delicate balance of interactions among system constituents. The emergence of discrete-time crystal (DTC) in typical many-body periodically driven systems occurs when there is a breaking of time translation symmetry. Coexisting coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at distinct regions have been investigated under the controlled spin rotational error of a disorder-free spin-1/2 chain for different types of spin-spin interactions. We contribute a novel approach for the emergence of the DTC-DMBL-chimeralike state, which is robust against external static fields in a periodically driven quantum many-body system.

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We investigate the non-equilibrium dynamics of a Heisenberg spin-1/2 chain driven by a periodic magnetic field. Based on its instantaneous integrability and inherent symmetry, we analytically study the magnetization and many-body tunneling (MBT). Both of them exhibit periodicity distinct from the driving period. The magnetization is shown to be independent of the initial state and robust against perturbations, signaling the formation of discrete time crystal (DTC) order. The DTC phase is found to be continuously tunable through magnetic field. The system exhibits perfect MBT, manifested as exactly vanishing Loschmidt echo (LE) thus divergent LE rate function at half period of the DTC. Remarkably, the perfect MBT is independent of the system size, and can be traced to an effective gap closure induced by quantum geometric effects. Furthermore, the Loschmidt echo spectra entropy shows logarithmic-dependence on system size, consistent with non-thermal nature of the DTC phase. We propose a protocol using ultracold atoms for experimental realization of the DTC and MBT.
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.
Periodically driven (Floquet) systems are described by time-dependent Hamiltonians that possess discrete time translation symmetry. The spontaneous breaking of this symmetry leads to the emergence of a novel non-equilibrium phase of matter—the Discrete Time Crystal (DTC). In this paper, we propose a scheme to extend the lifetime of a DTC in a paradigmatic model—a translation-invariant Ising spin chain with nearest-neighbor interaction J, subjected to a periodic kick by a transverse magnetic field with frequency 2πT. This system exhibits the hallmark signature of a DTC—persistent sub-harmonic oscillations with frequency πT—for a wide parameter regime. Employing both analytical arguments as well as exact diagonalization calculations, we demonstrate that the lifetime of the DTC is maximized, when the interaction strength is tuned to an optimal value, JT=π. Our proposal essentially relies on an interaction-induced quantum interference mechanism that suppresses the creation of excitations, and thereby enhances the DTC lifetime. Intriguingly, we find that the period doubling oscillations can last eternally in even size systems. This anomalously long lifetime can be attributed to a time reflection symmetry that emerges at JT=π. Our work provides a promising avenue for realizing a robust DTC in various quantum emulator platforms.
Discrete time crystals (DTCs) are non-equilibrium phases of matter that break the discrete time-translation symmetry and is characterized by a robust subharmonic response in periodically driven quantum systems. Here, we explore the DTC in a disorder-free, periodically kicked XXZ spin chain, which is stabilized by the Floquet strong Hilbert space fragmentation. We numerically show the period-doubling response of the conventional DTC order, and uncover a multiple-period response with beating dynamics due to the coherent interplay of multiple πππ-pairs in the Floquet spectrum of small-size systems. The lifetime of the DTC order exhibits independence of the driving frequency and a power-law dependence on the ZZ interaction strength. It also grows exponentially with the system size, as a hallmark of the strong fragmentation inherent to the Floquet model. We analytically reveal the approximate conservation of the magnetization and domain-wall number in the Floquet operator for the emergent strong fragmentation, which is consistent with numerical results of the dimensionality ratio of symmetry subspaces. The rigidity and phase regime of the DTC order are identified through finite-size scaling of the Floquet-spectrum-averaged mutual information, as well as via dynamical probes. Our work establishes the Floquet Hilbert space fragmentation as a disorder-free mechanism for sustaining nontrivial temporal orders in out-of-equilibrium quantum many-body systems.
We propose a novel protocol to realize discrete time-crystal (DTC) order in clean, periodically driven spin-1/21/21/2 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 (εr\varepsilon_rεr​), 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 εr\varepsilon_rεr​. In particular, the εr\varepsilon_rεr​ 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 nonequilibrium phases.
Periodically driven quantum systems host a range of non-equilibrium phenomena which are unrealizable at equilibrium. Discrete time-translational symmetry in a periodically driven many-body system can be spontaneously broken to form a discrete time crystal, a putative quantum phase of matter. We present the observation of discrete time crystalline order in a driven system of paramagnetic PPP -donor impurities in isotopically enriched 28Si^{28}Si28Si cooled below 101010 K. The observations exhibit a stable subharmonic peak at half the drive frequency which remains pinned even in the presence of pulse error, a signature of DTC order. We propose a theoretical model based on the paradigmatic central spin model which is in good agreement with experimental observations, and investigate the role of dissipation in the stabilisation of the DTC. Both experiment and theory indicate that the order in this system is primarily a dissipative effect, and which persists in the presence of spin-spin interactions. We present a theoretical phase diagram as a function of interactions and dissipation for the central spin model which is consistent with the experiments. This opens up questions about the interplay of coherent interaction and dissipation for time-translation symmetry breaking in many-body Floquet systems.
Abstract Chimera states are a captivating occurrence in which a system composed of multiple interconnected elements exhibits a distinctive combination of synchronized and desynchronized behavior. The emergence of these states can be attributed to the complex interdependence between quantum entanglement and the delicate balance of interactions among system constituents. The emergence of discrete-time crystal (DTC) in typical many-body periodically driven systems occurs when there is a breaking of time translation symmetry. Coexisting coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at distinct regions have been investigated under the controlled spin rotational error of a disorder-free spin-1/2 chain for different types of spin-spin interactions. We contribute a novel approach for the emergence of the DTC-DMBL-chimeralike state, which is robust against external static fields in a periodically driven quantum many-body system.