Quantum butterfly effect in polarized Floquet systems

TL;DR

This paper investigates quantum dynamics in polarized Floquet systems, comparing chaotic models and random circuits, revealing differences in diffusion and butterfly velocities due to quantum coherence effects.

Contribution

It demonstrates that random unitary circuits accurately predict butterfly velocities but not diffusion constants in polarized regimes, clarifying their applicability.

Findings

Random circuits predict butterfly velocity scaling correctly.

Random circuits fail to predict diffusion constant scaling.

Quantum coherence influences the butterfly effect slowdown.

Abstract

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 spacetime translation invariance) and random unitary circuits which vary both in space and time. We find that for small but finite polarization per length (in the thermodynamic limit), the random unitary circuit correctly predicts the scaling of the butterfly velocity but incorrectly predicts the scaling of 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 for non-random chaotic systems, and sheds light into the origin of the slow down of the butterfly effect in highly polarized systems or at low temperature.