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 ), the “butterfly velocity” of particle motion at low energies has an upper bound that must scale as , 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.
- Received 17 November 2023
- Revised 12 February 2024
- Accepted 5 March 2024
DOI:https://doi.org/10.1103/PhysRevB.109.094310
©2024 American Physical Society
Physics Subject Headings (PhySH)
Statistical Physics & ThermodynamicsQuantum Information, Science & Technology