Dynamically Frozen Floquet Quantum Matter: Ergodicity Breaking without Disorder in the Thermodynamic Limit

Ergodicity is at the heart of equilibrium Statistical Mechanics. The hypothesis has immediate implications in predicting generic behaviour of a system driven out of equilibrium. For example, ergodicity hypothesis implies, when a clean, quantum chaotic, many-body system is driven by varying a parameter of its Hamiltonian periodically in time, the system will heat up without bound. In the absence of any conservation law, the drive is expected to steer it towards a chaotic state described locally by an infinite-temperature ensemble. Here we present a generic counterexample to this premise. We show, a many-body system under strong periodic drive can dynamically freeze into non-trivial states due to emergence of certain approximate but perpetual conservation laws. As a striking demonstration, an infinite, clean, interacting, non-integrable many-body system is shown to exhibit zero growth of entanglement entropy density after being driven over several decades. Several aspects of the phenomena, including the energence of the conservation laws, pose new open puzzles that cannot be explained by conventional concepts. We will outline those in the talk.