SciPost Physics

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

• doi: 10.21468/SciPostPhys.9.2.024
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Wang, Exact dynamical correlations of hard-core anyons in one-dimensional lattices
  Phys. Rev. B 105, 205143 (2022) [Crossref]
• Sekania et al., Directional scrambling of quantum information in helical multiferroics
  Phys. Rev. B 104, 224421 (2021) [Crossref]
• Kuwahara et al., Absence of Fast Scrambling in Thermodynamically Stable Long-Range Interacting Systems
  Phys. Rev. Lett. 126, 030604 (2021) [Crossref]
• Yuan et al., Quantum information scrambling in quantum many-body scarred systems
  Phys. Rev. Research 4, 023095 (2022) [Crossref]
• Gong et al., Coarse-Grained Entanglement and Operator Growth in Anomalous Dynamics
  Phys. Rev. Lett. 128, 080602 (2022) [Crossref]
• Zhang et al., Anomalous quantum information scrambling for Z3 parafermion chains
  Phys. Rev. B 103, 195156 (2021) [Crossref]
• McCulloch et al., Operator spreading in the memory matrix formalism
  J. Phys. A: Math. Theor. 55, 274007 (2022) [Crossref]
• Riddell et al., Scaling at the out-of-time-ordered correlator wavefront: Free versus chaotic models
  Phys. Rev. B 108, L121108 (2023) [Crossref]