Quantum butterfly effect in polarized Floquet systems with conservation laws

We explore quantum dynamics in Floquet many-body systems with local conservation laws in one spatial dimension, focusing on sectors of the Hilbert space which are highly polarized. We numerically compare the predicted charge diffusion constants and quantum butterfly velocity of operator growth between models of chaotic Floquet dynamics (with discrete time translation invariance) and random unitary circuits which vary both in space and time. We find that for any non-zero polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the butterfly velocity but incorrectly predicts the diffusion constant. We argue that this is a consequence of quantum coherence on short time scales. Our work clarifies the settings in which random unitary circuits provide correct physical predictions, and the origin of the slow down of the butterfly effect in highly polarized systems.