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