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Locality bounds for quantum dynamics at low energy
- Source :
- Phys. Rev. B 109, 094310 March (2024)
- Publication Year :
- 2023
-
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.<br />Comment: 12 pages, 0 figures
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 109, 094310 March (2024)
- Publication Type :
- Report
- Accession number :
- edsarx.2310.02856
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.109.094310