The dynamics of generic closed many-body quantum systems is believed to be ergodic. A paradigmatic example is a quantum quench, which takes the system out of equilibrium. Local properties relax quickly and then approach the thermal equilibrium asymptotically, which can be sufficiently described via the eigenstate thermalization hypothesis (ETH). Alternatively, non-equilibrium dynamics can also be induced by time-dependent drives. In this setup, as energy conservation is absent, those systems normally keep absorbing energy and heat up to a featureless "infinite-temperature" state.
There has been great effort on the last decades to understand how to prevent many-body systems from thermalization. For time-independent systems, a prominent example is many-body localization (MBL) where all eigenstates deviate from the ETH prediction. The recent discovery of quantum many-body scars (QMBS) suggests that special ergodicity-breaking eigenstates can also appear in an otherwise thermalizing spectrum. Periodically driven or Floquet systems can also be non-ergodic. The driving induced heating can either be completely evaded via MBL, or significantly suppressed by using high frequency driving which can give rise to a transient but long-lived prethermal phenomenon.
This thesis introduces several new ergodicity-breaking phenomena in closed quantum many-body systems. First, an experimentally feasible protocol will be proposed to realize QMBS in optical lattices via Floquet engineering. Then I will show that QMBS in a fractionalized strongly correlated system can demonstrate the coexistence of persistent oscillations and the volume-law entanglement generation. Such a behavior is very counter-intuitive as within the ETH paradigm, volume-law scaling normally implies ergodic behavior. Similarly, in all previously identified models demonstrating persistent oscillations, the underlying QMBS only exhibits sub-extensive entanglement. The fact that Hamiltonians governing these non-ergodic phenomena always have time translation symmetry (TTS) naturally raises the question: Can systems without TTS also exhibit interesting non-ergodic collective phenomenon? Those systems can be expected to exhibit far richer dynamics, yet are also challenging to study due to the lack of Floquet theory. Nevertheless, I will provide affirmative answers to the above question by investigating both quasi-periodic and structured random drivings. For continuous quasi-periodic driving, the idea of the Floquet time spiral will be developed. This leads to a new non-equilibrium phase of matter — the discrete-time quasicrystal where quasi-TTS is spontaneously broken. I will finally introduce a new family of random driving protocols with a n multipolar structure. Although the TTS is completely broken due to the temporal randomness, I will show that a prethermal phenomenon still exists for high frequency driving similar to Floquet systems. This provides a sufficiently long time window to host novel non-equilibrium phases, e.g. a prethermal random multipolar discrete time crystal.