Locality bounds for quantum dynamics at low energy
| Autor: | Osborne, Andrew, Yin, Chao, Lucas, Andrew |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 109, 094310 March (2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.109.094310 |
| Popis: | 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. Comment: 12 pages, 0 figures |
| Databáze: | arXiv |
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