Floquet Time Crystals (1603.08001v4)

Abstract: We define what it means for time translation symmetry to be spontaneously broken in a quantum system, and show with analytical arguments and numerical simulations that this occurs in a large class of many-body-localized driven systems with discrete time-translation symmetry.

• The paper defines time-translation symmetry breaking (TTSB) in Floquet systems through rigorous theoretical constructs and numerical simulations.
• The study leverages many-body localization to reveal persistent oscillations at subharmonics in driven quantum systems.
• Numerical evidence from TEBD and exact diagonalization confirms that disorder sustains time-crystal behavior.

An Evaluation of "Floquet Time Crystals" in Quantum Systems

The paper "Floquet Time Crystals" presents a detailed analysis of time-translation symmetry breaking (TTSB) within the framework of many-body localized (MBL) driven quantum systems. Through both theoretical constructs and numerical simulations, the authors, Dominic V. Else, Bela Bauer, and Chetan Nayak, propose a novel definition of TTSB and demonstrate the existence of systems that embody this phenomenon. The work builds upon the growing body of literature surrounding time crystals and MBL systems, providing critical insights into the behavior of quantum systems beyond thermal equilibrium.

Key Contributions

1. Definition of TTSB: The authors establish a precise definition of what it means for a quantum system to exhibit TTSB, adapting the concept of spontaneous symmetry breaking (SSB) to temporal rather than spatial symmetries. The challenge in defining TTSB arises from the inherent time-independence of thermal equilibrium states. The authors circumvent this limitation by examining non-equilibrium conditions, asserting that TTSB can manifest in systems where the approach to thermal equilibrium is inhibited, notably within MBL systems.
2. Theoretical Construct: They propose that in a driven system, such as a Floquet system characterized by periodic driving, time evolution can lead to states that break TTS. Drawing analogies to spatial SSB, they construct definitions TTSB-1 and TTSB-2 to capture the essential characteristics of TTSB. TTSB-1 focuses on the observable manifestation under time evolution, while TTSB-2 relates to the structure of eigenstates in the Floquet spectrum.
3. Floquet-MBL Systems: The paper leverages the properties of MBL systems, where traditional thermalization fails, providing an ideal backdrop for TTSB. The authors employ analytical arguments to demonstrate that in such systems, eigenstates can be long-range correlated despite the presence of local integrals of motion.
4. Numerical Evidence: To substantiate their theoretical predictions, the authors undertake numerical simulations using TEBD and exact diagonalization methods. These simulations reveal persistent oscillations in systems driven at periodic intervals, supporting the claim of TTSB. They observe such systems responding at subharmonics of the driving frequency, further substantiating the time-crystal nature of these systems.

Strong Results and Implications

The paper's findings present several noteworthy numerical results, such as the persistent oscillations at halved frequencies of the driving force. These results are bolstered by simulations illustrating the resilience of these oscillations in the presence of disorder, a haLLMark of MBL systems.

The implications of this research are manifold:

• Theoretical Insight: This work pushes the boundaries of theoretical physics, suggesting new ways to understand non-equilibrium quantum dynamics. It implies that TTSB is a realistic phenomenon in nature, carrying potential consequences for understanding time in quantum contexts.
• Practical Applications: While direct applications in technology are speculative, such phenomena could eventually be harnessed in quantum computing or information storage, where time-symmetry properties might be exploited for novel functionalities.
• Future Research: The concepts and methodologies introduced challenge researchers to explore broader classes of quantum systems for similar behaviors. The stability of TTSB under perturbations invites further studies to identify other systems or conditions under which TTSB manifests.

Speculation on the Future of AI Developments

While the paper primarily concerns quantum physics, it indirectly resonates with AI research in material science and simulations. As AI techniques continue to evolve, they may become instrumental in simulating complex quantum systems and uncovering new phases of matter, including those akin to time crystals. Machine learning approaches might optimize the identification of state spaces conducive to TTSB or even predict the behavior of unknown quantum phases under various driving conditions. Overall, the confluence of AI with theoretical physics could accelerate discoveries in non-equilibrium quantum phases, potentially revolutionizing both fields.

In conclusion, this paper provides a robust theoretical and empirical foundation for the existence of Floquet time crystals, suggesting promising avenues for future exploration in quantum physics and beyond. Through careful definition, innovative analysis, and rigorous simulation, the authors convincingly argue for the existence and significance of time translation symmetry breaking in many-body localized systems.