  Chimera states are a captivating occurrence in which a system composed of
multiple interconnected elements exhibits a distinctive combination of
synchronized and desynchronized behavior. The emergence of these states can be
attributed to the complex interdependence between quantum entanglement and the
delicate balance of interactions among system constituents. The emergence of
discrete-time crystal (DTC) in typical many-body periodically driven systems
occurs when there is a breaking of time translation symmetry. Coexisting
coupled DTC and a ferromagnetic dynamically many-body localized (DMBL) phase at
distinct regions have been investigated under the controlled spin rotational
error of a disorder-free spin-1/2 chain for different types of spin-spin
interactions. We contribute a novel approach for the emergence of the
DTC-DMBL-chimeralike state, which is robust against external static fields in a
periodically driven quantum many-body system.
