Locality bounds for quantum dynamics at low energy
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914733798457344 |
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| author | Osborne, Andrew Yin, Chao Lucas, Andrew |
| author_facet | Osborne, Andrew Yin, Chao Lucas, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_02856 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Locality bounds for quantum dynamics at low energy Osborne, Andrew Yin, Chao Lucas, Andrew Mathematical Physics Strongly Correlated Electrons Quantum Physics 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. |
| title | Locality bounds for quantum dynamics at low energy |
| topic | Mathematical Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2310.02856 |