Discrete time crystals: rigidity, criticality, and realizations (1608.02589v3)

Abstract: Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.

• The paper demonstrates that periodic driving induces subharmonic oscillations and symmetry breaking in a one-dimensional quantum system.
• It employs numerical simulations to extract phase boundaries and finite-size scaling exponents that characterize the dynamical quantum phase transition.
• The study proposes an experimental realization using trapped ion systems to stabilize discrete time crystals against decoherence.

Overview of "Discrete time crystals: rigidity, criticality, and realizations"

The paper, "Discrete time crystals: rigidity, criticality, and realizations," presents a detailed exploration into the concept of discrete time crystals (DTCs), a quantum phase of matter that breaks discrete time translation symmetry in out-of-equilibrium periodically driven systems. These systems exhibit subharmonic oscillations with a period quantized to an integer multiple of the driving period, a phenomenon that originates from a synergy between many-body localization (MBL) and collective synchronization. The authors strip down a one-dimensional model displaying these properties and methodically investigate its robustness and criticality through numerical simulations.

One of the central focal points of this paper is the development of a DTC phase diagram, illustrating the effect of interaction strength and drive imperfections on the formation and stability of DTCs. The researchers identify a range of parameter space where the system maintains locked-in oscillations at half the driving frequency, even under perturbations. This rigidity is underscored by mapping out the breakdown of the DTC phase into a trivial Floquet insulator.

Key Numerical Results and Phase Transition Analysis

Through numerical simulations, the authors extract key signatures and phase boundaries characterizing the DTC. Among the metrics considered, the auto-correlation function's behavior is critical in signaling symmetry breaking, where robust oscillations at a fixed frequency indicate the presence of a DTC. Furthermore, the paper identifies fluctuations in the magnitude and variance of subharmonic peaks as an effective diagnostic tool for locating phase transitions.

Significantly, the paper explores the scaling properties of the dynamical quantum phase transition from a DTC phase to a paramagnetic phase. Using mutual information as a probe, the authors determine the finite-size scaling exponents associated with this transition, aligning with the Fisher random Ising universality class. The exploration includes the scaling collapse of numerically obtained critical properties, which supports the proposed theoretical framework.

Experimental Realization and Future Implications

The paper completes its discourse with a proposal for realizing discrete time crystals in experimental settings such as trapped ion systems. The authors argue that long-range interactions, inherent to trapped ion systems, can stabilize DTCs against decoherence and uniformly propose a realistic setup capable of exhibiting and detecting the haLLMark characteristics of a DTC. This is particularly relevant given the practical feasibility and technological advancements in these platforms.

In plotting a course for future experimental validation, the authors highlight the compatibility of their theoretical model with current quantum simulation capabilities. This not only serves to strengthen the prospects of observing DTCs in laboratory settings but also speaks to the broader applicability and adaptability of time crystal concepts in quantum technology.

Theoretical and Practical Implications

From a theoretical standpoint, this paper advances our understanding of non-equilibrium phases by presenting a coherent paper of time symmetry breaking driven by periodic perturbations. The underlying implications for symmetry and phase transitions in quantum systems contribute to ongoing discussions in condensed matter physics and quantum information science.

Practically, the realization of discrete time crystals could open new avenues for developing next-generation technologies exploring quantum coherence and synchronization phenomena. The insights provided by this research may also inform the control and manipulation techniques crucial for the development of more robust quantum computing and sensing applications.

In essence, this work broadens the horizon of quantum physics by detailing the intricate dynamics and realizations of discrete time crystals, while equipping the research community with tangible methodologies and insights necessary for the next phase of exploration in this domain.