Prethermal higher-order topological time crystals protected by emergent symmetry

In this talk, we introduce a prethermal higher-order topological time crystal in a two-dimensional many-body interacting spin system. We find that by adding high frequency driving, the static Hamiltonian, which is fully stabilized and topologically trivial, will arise higher-order corner modes protected by an emergent global $mathbb{Z}_2 imes mathbb{Z}_2$ symmetry in the prethermal region. The sub-harmonic oscillations of the magnetization at corners, in contrast to those rapidly vanish in the bulk and edges, characterizing the breaking of discrete time-translation symmetry at higher-order topological corner modes. With sufficiently high driving frequency, these modes exhibit robustness against small local perturbations, even for those that anti-commute with the global symmetry. Before thermalization, a transient beating behaviour of the magnetization in the bulk and edge spins is observed and explained. In addition, we show that the lifetime of such a phase scales exponentially with the driving frequency. We further propose an experiment to realize this phase with superconducting qubits, where five-body interactions inherent to our model can be implemented through digital simulation in an analytical fashion.