Boundary discrete time crystals induced by topological superconductors in solvable spin chains

Floquet time crystal, which breaks discrete time-translation symmetry, is an intriguing phenomenon in non-equilibrium systems. It crucial to understand the rigidity and robustness of crystal (DTC) phases a many-body system, finding precisely solvable model can pave way for understanding DTC phase. Here, we propose study spin chain by mapping it superconductor through Jordan-Wigner transformation. The phase diagrams topological systems are characterized invariants tell existence anomalous edge states. sub-harmonic oscillation, typical signal DTC, be generated from such states protected topology. We also examine adding symmetry-preserving symmetry-breaking perturbations. Our results on topologically provide deep when generalized other interacting or dissipative