Stability of slow Hamiltonian dynamics from Lieb-Robinson bounds
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910691199287296 |
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| author | Toniolo, Daniele Bose, Sougato |
| author_facet | Toniolo, Daniele Bose, Sougato |
| contents | We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is stable against generic, even time-dependent, local perturbations. The sum of these perturbations can cover a significant amount of the system's size. The stability of the slow dynamics follows from proving that the Lieb-Robinson bound for the dynamics of the total Hamiltonian is the sum of two contributions: the Lieb-Robinson bound of the unperturbed dynamics and an additional term coming from the Lieb-Robinson bound of the perturbations with respect to the unperturbed Hamiltonian. Our results are particularly relevant in the context of the study of the stability of Many-Body-Localized systems, implying that if a so called ergodic region is present in the system, to spread across a certain distance it takes a time proportional to the exponential of such distance. The non-perturbative nature of our result allows us to develop a dual description of the dynamics of a system. As a consequence we are able to prove that the presence of a region of disorder in a ergodic system implies the slowing down of the dynamics in the vicinity of that region. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05958 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of slow Hamiltonian dynamics from Lieb-Robinson bounds Toniolo, Daniele Bose, Sougato Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons Mathematical Physics We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is stable against generic, even time-dependent, local perturbations. The sum of these perturbations can cover a significant amount of the system's size. The stability of the slow dynamics follows from proving that the Lieb-Robinson bound for the dynamics of the total Hamiltonian is the sum of two contributions: the Lieb-Robinson bound of the unperturbed dynamics and an additional term coming from the Lieb-Robinson bound of the perturbations with respect to the unperturbed Hamiltonian. Our results are particularly relevant in the context of the study of the stability of Many-Body-Localized systems, implying that if a so called ergodic region is present in the system, to spread across a certain distance it takes a time proportional to the exponential of such distance. The non-perturbative nature of our result allows us to develop a dual description of the dynamics of a system. As a consequence we are able to prove that the presence of a region of disorder in a ergodic system implies the slowing down of the dynamics in the vicinity of that region. |
| title | Stability of slow Hamiltonian dynamics from Lieb-Robinson bounds |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons Mathematical Physics |
| url | https://arxiv.org/abs/2405.05958 |