Dynamical Scarring from Scrambling in Two Dimensional Topological Materials

TL;DR

This paper investigates how information scrambling behaves in two-dimensional topological materials, revealing that edge modes cause dynamical scarring where information travels along edges without full scrambling.

Contribution

It demonstrates that chiral and helical edge modes induce dynamical scarring, affecting information spreading and revealing directional dependence in topological models.

Findings

Edge modes cause information to travel along boundaries without complete scrambling.

The butterfly velocity in the bulk depends on lattice direction.

Edge scars pass through each other without interaction.

Abstract

Out-of-time ordered correlators are a probe of how the information of an initial perturbation is effectively scrambled under unitary time evolution, widely used to study quantum chaos. They have also been used to demonstrate that information is trapped in the zero dimensional edge modes of topological insulators and superconductors, and does not become scrambled. Here we study scrambling in two dimensional topological models. In the bulk the butterfly velocity, the speed at which the out-of-time ordered correlator spreads, gains a directional dependence from the underlying lattice. Furthermore when there are chiral or helical edge modes present these cause a form of dynamical scarring. The information about an initial perturbation on the boundary of the system travels around the edge, carried by the edge modes, but is not scrambled over very long time scales. The direction and speed of the scars are given by the velocities of the linearly dispersing edge modes. We further show that these scars do not interact, passing through each other. We back up these results with analytical and numerical calculations on exemplary models.