Asymmetric butterfly velocities in 2-local Hamiltonians

TL;DR

This paper introduces simple 2-local Hamiltonian models on a 1D lattice that demonstrate asymmetric butterfly velocities, revealing directional differences in information spreading in quantum systems.

Contribution

The authors construct and analyze 2-local Hamiltonians exhibiting asymmetric butterfly velocities, providing a clear understanding of directional operator spreading in quantum hydrodynamics.

Findings

Models show asymmetric butterfly velocities between left and right directions.

Asymmetry is explained via quasiparticle velocities in a free limit.

Provides insight into directional information propagation in quantum systems.

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.