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

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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 outoftimeordered 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 2local 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 (noninteracting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.
Mr Zhang: "We thank the referee for their..."
in Report on Asymmetric butterfly velocities in 2local Hamiltonians