Chimera Time-Crystalline order in quantum spin networks

Symmetries are well known to have had a profound role in our understanding of nature and are a critical design concept for the realization of advanced technologies. In fact, many symmetry-broken states associated with different phases of matter appear in a variety of quantum technology applications. Such symmetries are normally broken in spatial dimension, however they can also be broken temporally leading to the concept of discrete time symmetries and their associated crystals. Discrete time crystals (DTCs) are a novel state of matter emerging in periodically-driven quantum systems. Typically, they have been investigated assuming individual control operations with uniform rotation errors across the entire system. In this work we explore a new paradigm arising from non-uniform rotation errors, where two dramatically different phases of matter coexist in well defined regions of space. We consider a quantum spin network possessing long-range interactions where different driving operations act on different regions of that network. What results from its inherent symmetries is a system where one region is a DTC, while the second is ferromagnetic. We envision our work to open a new avenue of research on Chimera-like phases of matter where two different phases coexist in space.