Executive Summary : | Periodically driven quantum systems (Floquet systems) are versatile and can be used to realize inherently non-equilibrium quantum phases, such as Floquet time crystals (FTCs). FTCs break the discrete time-translation-symmetry of the drive, resulting in a persistent sub-harmonic response of physical observables. However, heating is ubiquitous in Floquet systems, posing a major challenge to realizing a FTC. Despite progress, much work still needs to be done to uncover the rich physics of these systems, particularly exploring intertwined space-time long-range order in many-body systems. This project aims to explore routes to realize Floquet phases of matter with hitherto unexplored intertwined spatiotemporal order. The project will focus on the dynamics of the "Floquet Space-Time Crystal" (FSTC), where both space and time translation symmetries are spontaneously broken. The project will explore three inter-related directions: examining FSTCs in systems with long-range interactions both in space and time, studying the effect of interactions on topological FSTCs protected by non-symmorphic space-time symmetries like "time glides," and exploring the dynamics of FSTCs in the presence of dissipation. The project will lead to a considerable enhancement of our understanding of spatiotemporally ordered states in periodically driven quantum systems, as well as the possibility of realizing other forms of temporal order such as "Time Quasicrystals." |