Prethermal Time-Crystalline Corner Modes

Understand

We demonstrate the existence of prethermal discrete time crystals whose sub-harmonic response is entirely localized to zero-dimensional corner modes.

• Within the exponentially long prethermal regime, we show that the robustness of these corner modes arises from two related, yet distinct mechanisms: the presence of a higher-order symmetry-protected topological phase in the effective Hamiltonian, or the emergence of a dynamical constraint that prevents the decay of the corner mode.
• While the first mechanism ensures the stability of the sub-harmonic response throughout the entirety of the prethermal regime, it is restricted to initial states in the ground state manifold of the effective Hamiltonian.
• By contrast, the second mechanism enables the observation of the prethermal time-crystalline order for arbitrary initial states, albeit with a time scale that is not only determined by the frequency of the drive, but also the relative energy scale across the system's sublattices.