Time crystals in interacting systems

01.09.2024 bis 31.08.2026

Time crystals, discrete (DTCs) and continuous (CTCs), are recently introduced non-equilibrium phases of matter that spontaneously break the time translational symmetry. Despite the recent advancement in theoretical understanding of this novel phase of matter, the time crystals in real-world experiments are stable only for short time scales. This results from quantum fluctuations and the instabilities of the experimental setups. A mechanism to stabilize the time crystal phase in such fluctuations has yet to be identified. This proposal intends to address these limitations by including experimental instabilities in theoretical models and devise methods to mitigate those detrimental effects. The main objective of this proposal is to theoretically investigate the existence of time crystals in interacting systems where coherent interaction might lead to stable phases in experiments. This includes studying the effect of experimental irregularities like anisotropic coupling and short-range interaction on the time crystalline phase of such interacting models. Another important objective of this proposal is to study the seeding effect in DTCs by analyzing the dynamics of coupled DTCs in both open and closed quantum systems. This is relevant and fundamental since the coupled dynamics of the DTCs have yet to be explored. It also extends to study the seeding effects in interacting models, which earlier have been limited to non-interacting systems. This will ensure the robustness of the seeding effect in time crystals and provide future directions for implementable technologies. This proposal furthermore comprises investigating time crystallization using the measurement process in long-range interacting systems, which thus far have been limited to central spin models. Measurement-induced phase transitions have garnered an extraordinary amount of interest due to the durability of many-body phases even in the presence of repeated measurements, and are compelling from the perspective of experiments.