Locality bounds for quantum dynamics at low energy

• URL: http://arxiv.org/abs/2310.02856v3
• Date: Fri, 29 Mar 2024 16:47:21 GMT
• Title: Locality bounds for quantum dynamics at low energy
• Authors: Andrew Osborne, Chao Yin, Andrew Lucas,
• Abstract summary: We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. For certain classes of Hamiltonians, the butterfly velocity" of particle motion at low energies has an upper bound that must scale as $E(2k-1)/2k$, as expected from dimensional analysis.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We discuss the generic slowing down of quantum dynamics in low energy density states of spatially local Hamiltonians. Beginning with quantum walks of a single particle, we prove that for certain classes of Hamiltonians (deformations of lattice-regularized $H\propto p^{2k}$), the ``butterfly velocity" of particle motion at low energies has an upper bound that must scale as $E^{(2k-1)/2k}$, as expected from dimensional analysis. We generalize these results to obtain bounds on the typical velocities of particles in many-body systems with repulsive interactions, where for certain families of Hubbard-like models we obtain similar scaling.

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