Muñoz de Nova, Juan RamónSols Lucía, Fernando2023-06-222023-06-222022-04-072469-992610.1103/PhysRevA.105.043302https://hdl.handle.net/20.500.14352/71489©2022 American Physical Society We are very grateful to I. Carusotto for stimulating discussions. We also thank useful comments from C. Creffield, I. Zapata, S. Finazzi, M. Płodzie´n, D. Wild, F. Michel, and, especially, R. Parentani, to whose memory we devote this work. This project has received funding from Grant No. FIS2017-84368-P from Spain’s MINECO, and from European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 847635.We propose the concept of a spontaneous many-body Floquet state. This is a state that, in the absence of external periodic driving, self-oscillates like in the presence of a periodic Hamiltonian, this behavior being spontaneously induced by many-body interactions. In addition, its quantum fluctuations are described by regular Floquet theory. Furthermore, it is also a time crystal, presenting long-range time-periodic order. However, this crystalline behavior is very different to that of conventional Floquet discrete time crystals: here, there is no external periodic driving, energy is conserved, and the nature of the spontaneous symmetry breaking is continuous instead of discrete. We demonstrate that spontaneous many-body Floquet states can emerge in a variety of canonical many-body problems, ranging from interacting fermions to Bose-Hubbard models. We specifically show that a spontaneous many-body Floquet state is a universal intrinsic state of a one-dimensional flowing atom condensate, both subsonic and supersonic, resulting from a dynamical phase transition and robust against external perturbations and quantum fluctuations, proposing also realistic experimental scenarios for its observation. A spontaneous many-body Floquet state not only represents a realization of a continuous time crystal, but also another paradigm in Floquet physics.engjournal articlehttp://dx.doi.org/10.1103/PhysRevA.105.043302https://journals.aps.org/open access538.9OpticsPhysicsAtomicMolecularChemicalFísica de materialesFísica del estado sólido2211 Física del Estado Sólido