Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete) time semicrystal phase emerges with persistent temporal order in disorder, bridging discrete time crystals and fully disordered regimes. This phase exhibits a periodic skeleton, with discrete subharmonic peaks persisting atop a continuous spectrum. We extract a critical scaling behavior across the discrete time crystal to time semicrystal transition. Furthermore, even dynamical transitions between distinct periodic skeletons can be clearly identified with systematic log-periodic corrections to power-law scaling, revealing discrete scale invariance. These findings in holography significantly enrich the platforms for studying nonequilibrium phases of matter.
Understanding how temporal order degrades in quantum systems remains a central issue in nonequilibrium physics. Here we study the melting of discrete time crystals in a periodically driven holographic system, where a distinct (discrete) time semicrystal phase emerges with persistent temporal order in disorder, bridging discrete time crystals and fully disordered regimes. This phase exhibits a periodic skeleton, with discrete subharmonic peaks persisting atop a continuous spectrum. We extract a critical scaling behavior across the discrete time crystal to time semicrystal transition. Furthermore, even dynamical transitions between distinct periodic skeletons can be clearly identified with systematic log-periodic corrections to power-law scaling, revealing discrete scale invariance. These findings in holography significantly enrich the platforms for studying nonequilibrium phases of matter.
The stability of a discrete time crystal against thermal fluctuations has been studied numerically by solving a stochastic Landau-Lifshitz-Gilbert equation of a periodically driven classical system composed of interacting spins, each of which couples to a thermal bath. It is shown that in the thermodynamic limit, even though the long-range temporal crystalline order is stable at low temperature, it is melting above a critical temperature, at which the system experiences a nonequilibrium phase transition. The critical behaviors of the continuous phase transition have been systematically investigated, and it is shown that despite the genuine nonequilibrium feature of such a periodically driven system, its critical properties fall into the three-dimensional Ising universality class with a dynamical exponent (z=2) identical to that in the critical dynamics of a kinetic Ising model without driving.
The classification of phases of matter has been revolutionised by topological order and nonequilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"-non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipativeprotected quantum memory and novel non-equilibrium quantum phenomena.
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 P -donor impurities in isotopically enriched 28Si cooled below 10 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.
Discrete time quasicrystals (DTQC) constitute a class of non-equilibrium matter characterized by temporal order without strict periodicity, in contrast to conventional time crystals. Investigating these phenomena is essential for expanding our fundamental understanding of far-from-equilibrium quantum matter and spontaneous symmetry breaking beyond periodic regimes. Here, we experimentally observe a DTQC in a driven-dissipative ensemble of strongly interacting Rydberg atoms, displaying non-equilibrium dynamical response with a different finite Abelian group symmetry Zm×Zn. By applying a quasiperiodic drive using a dual-frequency drive with incommensurate frequencies, we demonstrate that the system exhibits a robust subharmonic response at multiple incommensurate frequencies, signifying the emergence of a DTQC phase. We map the full phase diagram of the system, which includes the DTQC phase, and demonstrate its rigidity against perturbations in both RF field intensity and laser detuning. Moreover, we observe a cyclic group symmetry effect that constrains the construction of Z2×Z3-symmetric DTQC. This work establishes a versatile platform for studying non-equilibrium phases of matter and provides insights into the dynamics of time-translation symmetry breaking in quantum many-body systems. Time-crystal phases have raised both theoretical and experimental interest across various platforms. Here, the authors report the observation of a discrete time-quasicrystal in a driven-dissipative ensemble of interacting Rydberg atoms, advancing the understanding of symmetry breaking in these systems.
The classification of phases of matter has been revolutionised by topological order and non equilibrium phenomena such as time crystals. However, a unified framework connecting temporal order, topology, and dissipation remains elusive. Here we introduce the concept of "Time-Quasicrystals"—non-equilibrium topological phases that exhibit quasi-periodic temporal order protected by dissipative dynamics. These phases emerge in driven dissipative quantum systems through the interplay of Floquet engineering and non-local dissipation, leading to an effective non-Hermitian Floquet Hamiltonian with topological edge modes in the frequency domain. We demonstrate three hallmarks of Time-Quasicrystals: (1) fractal-like temporal correlations with multiple incommensurate frequencies, (2) a quantised topological invariant robust against disorder, and (3) algebraically decaying memory of phase perturbations. We provide explicit experimental realisations in Rydberg atom arrays and circuit quantum electrodynamics platforms. Our work establishes Time-Quasicrystals as a bridge between topological phases, time crystals, and quantum simulation, opening pathways to dissipative protected quantum memory and novel non-equilibrium quantum phenomena.
Abstract The discovery of time crystals and topological phases has fundamentally altered our understanding of quantum matter, yet a unified framework that combines temporal quasi-order, topological protection, and engineered dissipation remains a central challenge. Here we introduce Floquet-engineered dissipative time quasicrystals (FDTCs) —a class of nonequilibrium topological phases that emerge from the synergy of quasi-periodic driving, non-local dissipation, and non-Hermitian topology. Using a combination of Floquet-Lindblad theory and frequency-space topology, we demonstrate that FDTCs exhibit three defining hallmarks: (i) fractal temporal correlations with multiple incommensurate frequencies, (ii) a quantized topological invariant robust against disorder, and (iii) algebraically decaying memory of phase perturbations—a signature of intrinsic protection. We establish a general theoretical framework mapping quasi-periodically driven dissipative systems to non-Hermitian tight-binding models on synthetic frequency lattices, revealing topological edge modes in the frequency domain that manifest as persistent temporal order. We provide explicit experimental blueprints for two leading quantum platforms: parametrically driven superconducting qubit arrays and Rydberg atom chains with structured dissipation. Numerical simulations validate the phase diagram, showing that FDTCs occupy a distinct region bounded by trivial dissipative dynamics, conventional time crystals, and thermal phases. Our work establishes FDTCs as a bridge between topological matter, non-equilibrium physics, and quantum simulation, opening pathways to dissipationprotected quantum memory, topologically robust frequency combs, and novel non-Hermitian quantum technologies.