Information scrambling and entanglement dynamics in Floquet Time Crystals

TL;DR

This paper investigates how information spreads and entanglement evolves in disordered Floquet time crystals, revealing unique directional dynamics and slow thermalization processes that differ from conventional many-body localized systems.

Contribution

It introduces a detailed analysis of OTOC and entanglement dynamics in Floquet time crystals, highlighting a quasi-protected direction and complex scrambling behavior.

Findings

OTOC spreads with different timescales along specific directions

Logarithmic growth of entanglement entropy over time

Universal scrambling rate after wavefront propagation

Abstract

We study the dynamics of out-of-time-ordered correlators (OTOCs) and entanglement of entropy as quantitative measures of information propagation in disordered many-body systems exhibiting Floquet time-crystal (FTC) phases. We find that OTOC spreads in the FTC with different characteristic timescales due to the existence of a preferred ``quasi-protected'' direction - denoted as $\ell$-bit direction - along which the spins stabilize their period-doubling magnetization for exponentially long times. While orthogonal to this direction the OTOC thermalizes as an usual MBL time-independent system (at stroboscopic times), along the $\ell$-bit direction the system features a more complex structure. The scrambling appears as a combination of an initially frozen dynamics (while in the stable period doubling magnetization time window) and a later logarithmic slow growth (over its decoherence regime) till full thermalization. Interestingly, in the late time regime, since the wavefront propagation of correlations has already settled through the whole chain, scrambling occurs at the same rate regardless of the distance between the spins, thus resulting in an overall envelope-like structure of all OTOCs, independent of their distance, merging into a single growth. Alongside, the entanglement entropy shows a logarithmic growth over all time, reflecting the slow dynamics up to a thermal volume-law saturation.