From time crystals to time quasicrystals: Exploring novel phases in transverse field Ising chains

Abstract: Time crystals (TCs) and time quasicrystals (TQCs) represent novel phases of matter that arise from the breaking of time translational symmetry in periodically and quasiperiodically driven quantum systems. In this study, we explore the formation of a TQC phase within the disordered quantum Ising chain model under a transverse field (ITF). Notably, TQCs demonstrate robust subharmonic responses at multiple incommensurate frequencies, unlike traditional TCs which respond at a single frequency. Our analysis reveals that the TQC phase exhibits stable magnetization responses even in the presence of interaction perturbations and imperfections in the quasiperiodic driving fields. Employing exact diagonalization techniques, we find that increasing the chain length further stabilizes both TC and TQC phases. These results suggest promising pathways for experimental realization of TQCs in cold atomic systems and quantum simulators, opening avenues for deeper investigation into these intriguing dynamical phenomena.