The interplay of disorder and interactions leads to many-body localization (MBL) which provides the only known generic mechanism for strong breakdown of thermalization in a closed quantum system. This phenomenon can protect exotic quantum order (in space and time) even at infinite temperature, leading to emergent nonergodic phases of matters with no equilibrium counterpart. In this talk, I will show that nonergodic dynamics, and the resulting localization protected order, can be found in minimal models dropping the essential ingredients needed for the existence of MBL. As a first example, I identify the absence of thermalization in a family of disorder-free, self-correcting quantum memories whose elementary excitations are associated with Abelian anyons. Our analysis reveals that mutual braiding statistics between anyons is suffice to intrinsically suppress the diffusion of anyons for an exponentially long time. The self-localization of anyons can impede logical errors, which in turn paves the way for identifying stable, low-dimensional quantum memories. I then turn to investigating a clean Floquet model whose quasi-energy spectrum conforms to the ergodic Wigner-Dyson distribution, yet with an unexpectedly robust, long-lived time-crystalline dynamics in the absence of disorder or fine-tuning. We related such behavior to a measure zero set of non-thermal Floquet eigenstates with long-range spatial correlations, which coexist with otherwise thermal states at infinite temperature and resemble the notion of "Floquet scars". We dubbed such a homogeneous time crystal formed in partially nonergodic systems, scarred discrete time crystal, which is distinct by nature from those stabilized by either many-body localization or prethermalization mechanism.