Discrete time crystals detected by time-translation twist

Abstract

We introduce a boundary condition twisted by time translation as a novel probe to characterize dynamical phases in periodically driven (Floquet) quantum systems. Inspired by twisted boundary conditions in equilibrium systems, this approach modifies the temporal evolution of the system upon completing a spatial loop, enabling the identification of distinct Floquet phases, including discrete time crystals (DTCs). By studying the spectral form factor (SFF) and its response to the twist, we uncover signatures of time-crystalline order, which exhibits periodic dependence on the twist parameter analogous to the Little-Parks effect in superconductors. We apply this framework to the kicked Ising model, demonstrating that our twist can distinguish time-crystalline phases.