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arXiv · 2310.02856

Locality bounds for quantum dynamics at low energy

Andrew Osborne·Chao Yin·Andrew Lucas
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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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Andrew Osborne, Chao Yin, Andrew Lucas. 2023-10-04. Locality bounds for quantum dynamics at low energy. https://doi.org/10.1103/physrevb.109.094310

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