Critical properties of the prethermal Floquet Time Crystal
- URL: http://arxiv.org/abs/2103.10818v2
- Date: Fri, 25 Jun 2021 14:37:33 GMT
- Title: Critical properties of the prethermal Floquet Time Crystal
- Authors: Muath Natsheh, Andrea Gambassi, Aditi Mitra
- Abstract summary: We investigate the critical properties characterizing the formation of the Floquet time crystal in the prethermal phase.
In particular, we focus on the critical line separating the trivial phase with period synchronized dynamics and absence of long-range spatial order.
The functional form of the aging is found to depend on whether the system is probed at times that are small or large compared to the drive period.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The critical properties characterizing the formation of the Floquet time
crystal in the prethermal phase are investigated analytically in the
periodically driven $O(N)$ model. In particular, we focus on the critical line
separating the trivial phase with period synchronized dynamics and absence of
long-range spatial order from the non-trivial phase where long-range spatial
order is accompanied by period-doubling dynamics. In the vicinity of the
critical line, with a combination of dimensional expansion and exact solution
for $N\to\infty$, we determine the exponent $\nu$ that characterizes the
divergence of the spatial correlation length of the equal-time correlation
functions, the exponent $\beta$ characterizing the growth of the amplitude of
the order-parameter, as well as the initial-slip exponent $\theta$ of the aging
dynamics when a quench is performed from deep in the trivial phase to the
critical line. The exponents $\nu, \beta, \theta$ are found to be identical to
those in the absence of the drive. In addition, the functional form of the
aging is found to depend on whether the system is probed at times that are
small or large compared to the drive period. The spatial structure of the
two-point correlation functions, obtained as a linear response to a perturbing
potential in the vicinity of the critical line, is found to show algebraic
decays that are longer ranged than in the absence of a drive, and besides being
period-doubled, are also found to oscillate in space at the wave-vector
$\omega/(2 v)$, $v$ being the velocity of the quasiparticles, and $\omega$
being the drive frequency.
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