Critical properties of the Floquet time crystal within the Gaussian approximation

Abstract

The periodically driven O(N) model is studied near the critical line separating a disordered paramagnetic phase from a period doubled phase, the latter being an example of a Floquet time crystal. The time evolution of one-point and two-point correlation functions are obtained within the Gaussian approximation and perturbatively in the drive amplitude. The correlations are found to show not only period doubling, but also power-law decays at large spatial distances. These features are compared with the undriven O(N) model, in the vicinity of the paramagnetic-ferromagnetic critical point. The algebraic decays in space are found to be qualitatively different in the driven and the undriven cases. In particular, the spatio-temporal order of the Floquet time crystal leads to position-momentum and momentum-momentum correlation functions which are more long-ranged in the driven than in the undriven model. The light-cone dynamics associated with the correlation functions is also qualitatively different as the critical line of the Floquet time crystal shows a light-cone with two distinct velocities, with the ratio of these two velocities scaling as the square-root of the dimensionless drive amplitude. The Floquet unitary, which describes the time evolution due to a complete cycle of the drive, is constructed for modes with small momenta compared to the drive frequency, but having a generic relationship with the square-root of the drive amplitude. At intermediate momenta, which are large compared to the square-root of the drive amplitude, the Floquet unitary is found to simply rotate the modes. On the other hand, at momenta which are small compared to the square-root of the drive amplitude, the Floquet unitary is found to primarily squeeze the modes, to an extent which increases upon increasing the wavelength of the modes, with a power-law dependence on it.

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Cited by in corpus (13)

• Classical approaches to prethermal discrete time crystals in one, two, and three dimensions
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Emergent parametric resonances and time-crystal phases in driven BCS systems
• Floquet time crystals in driven spin systems with all-to-all $p$-body interactions
• Dynamical phases transitions in periodically driven Bardeen-Cooper-Schrieffer systems
• Critical properties of the prethermal Floquet Time Crystal
• Fractal nature of high-order time crystal phases
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• Floquet topological systems with flat bands: Edge modes, Berry curvature, and Orbital magnetization
• Discrete time crystals in Bose-Einstein Condensates and symmetry-breaking edge in a simple two-mode theory
• Orbital magnetization of Floquet topological systems