Prethermal Time-Crystalline Corner Modes

TL;DR

This paper demonstrates the existence of prethermal discrete time crystals localized at corner modes, with robustness arising from topological phases or dynamical constraints, in a 2D spin model.

Contribution

It introduces two mechanisms for stabilizing prethermal time-crystalline corner modes, expanding understanding of their robustness and initial state dependence.

Findings

Corner modes exhibit sub-harmonic response localized at zero-dimensional corners.

Robustness from higher-order topological phases or dynamical constraints.

Simulation of a 2D spin model confirms theoretical mechanisms.

Abstract

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. We characterize these two mechanisms by simulating the dynamics of a periodically driven two-dimensional spin model, and discuss natural extensions of our model to all other dimensions.