On Lieb-Robinson bounds for a class of continuum fermions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916336511221760 |
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| author | Hinrichs, Benjamin Lemm, Marius Siebert, Oliver |
| author_facet | Hinrichs, Benjamin Lemm, Marius Siebert, Oliver |
| contents | We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincaré 21.11 (2020)]. We provide a Lieb-Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb-Robinson bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17736 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Lieb-Robinson bounds for a class of continuum fermions Hinrichs, Benjamin Lemm, Marius Siebert, Oliver Mathematical Physics Quantum Physics We consider the quantum dynamics of a many-fermion system in $\mathbb R^d$ with an ultraviolet regularized pair interaction as previously studied in [M. Gebert, B. Nachtergaele, J. Reschke, and R. Sims, Ann. Henri Poincaré 21.11 (2020)]. We provide a Lieb-Robinson bound under substantially relaxed assumptions on the potentials. We also improve the associated one-body Lieb-Robinson bound on $L^2$-overlaps to an almost ballistic one (i.e., an almost linear light cone) under the same relaxed assumptions. Applications include the existence of the infinite-volume dynamics and clustering of ground states in the presence of a spectral gap. We also develop a fermionic continuum notion of conditional expectation and use it to approximate time-evolved fermionic observables by local ones, which opens the door to other applications of the Lieb-Robinson bounds. |
| title | On Lieb-Robinson bounds for a class of continuum fermions |
| topic | Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2310.17736 |