## Asymmetric butterfly velocities in 2-local Hamiltonians

Yong-Liang Zhang, Vedika Khemani

SciPost Phys. 9, 024 (2020) · published 25 August 2020

### Abstract

The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.
Funder for the research work leading to this publication