The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
We report on the first experimental observation of a non-equilibrium phase of matter, the discrete time crystal (DTC). A DTC breaks time-translational symmetry and displays spatio-temporal quantum order in all of its eigenstates, a feature dubbed “eigenstate order”. We implement Floquet dynamics on a 1D chain of 20 superconducting qubits [2]. Engineered disorders in the two-qubit couplings allow many-body localization (MBL) to occur despite strong external drive, thereby stabilizing the non-equilibrium phase [3]. We carefully validate the phase structure of the DTC by probing the average response of all eigenstates belonging to the Floquet unitary. Using a suitable choice of order parameter, we further identify the location of the MBL-ergodicity crossover via experimentally observed finite-size effects. These results open a direct path to studying quantum phase transitions and critical phenomena on NISQ quantum processors.
A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.
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 π-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.
Discrete time crystals (DTCs) have emerged as novel nonequilibrium phases of matter that spontaneously break discrete time-translation symmetry in periodically driven systems. Rigorous experimental validation of DTCs, which requires highly controllable quantum simulators, has stimulated extensive research across diverse fields in condensed matter physics and quantum information technologies. Among these advances, DTCs were demonstrated in a hybrid spin register within diamond, comprising a processor spin and surrounding memory spins. However, in conventional strategies involving a bias magnetic field, the field application effectively restricts the controllability of the processor spin. This limitation can be a significant barrier to the next goal of DTCs: achieving multifunctionality through enhanced local controllability. In this study, we theoretically propose multiple DTC protocols through the design of specific single-site control within the entire system. To this end, we consider a concrete model of a diamond-based quantum simulator operating without a bias magnetic field, thereby eliminating the restrictions on the processor spin. Our findings demonstrate that single-site operations enable access to DTCs with multiple distinct features in terms of periodicity and lifetime. Therefore, this approach provides a promising platform for creating diverse DTCs induced by single-site operations.
A discrete time crystal (DTC) is an out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Previous studies have been limited to a set of models with Ising-like couplings - and mostly only in one dimension - thus precluding our understanding of the existence (or not) of DTCs in models with more realistic interactions. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. We uncover a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, and identify the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.
A discrete time crystal is an out-of-equilibrium phase of matter characterized by the spontaneous breaking of discrete time-translation symmetry. Using extensive numerical simulations based on matrix-product-state methods, we provide evidence for discrete time-crystalline behavior in strongly disordered spin chains with Heisenberg interactions, including the isotropic point, subject to periodic driving. Starting from a many-body localized regime, we observe that rotations induced by delta kicks produce a pronounced subharmonic response at half the drive frequency in spin observables. We investigate the stability of this response against rotation-angle errors through entanglement entropy, quantum Fisher information, short-range spin correlations, and restricted-control ergotropy. Increasing the rotation error reveals an intermediate dynamical regime separating the time-crystalline and Floquet-localized responses. In this regime, most observables exhibit signatures of weakly correlated dynamics reminiscent of Anderson localization.