Logarithmic lightcones in the multiparticle Anderson model with sparse interactions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915475035783168 |
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| author | Toniolo, Daniele Bose, Sougato |
| author_facet | Toniolo, Daniele Bose, Sougato |
| contents | We prove that the dynamics of the one-dimensional $ XY $ model with random magnetic field perturbed by a sparse set of $ ZZ $ terms with a large coupling constant $ Δ$ gives rise to Lieb-Robinson (L-R) bounds with a logarithmic lightcone and amplitude proportional to $ Δ^{-1} $. These spin systems are equivalent to a set of spinless lattice fermions subjected to a random on site potential and sparse density-density interactions. In the absence of the random magnetic field we also obtain a suppression of the L-R bounds as $ Δ^{-1} $. These results follow from the application of a general theorem about the L-R bound of a generic local time-dependent one-dimensional spin system with local time-dependent perturbations. Adopting the interaction picture of the dynamics, the large and sparse $ ZZ $ perturbations of the $ XY $ model, with or without disorder, are mapped into high-frequency periodic perturbations. All our results are non-perturbative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02383 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Logarithmic lightcones in the multiparticle Anderson model with sparse interactions Toniolo, Daniele Bose, Sougato Mathematical Physics Disordered Systems and Neural Networks Quantum Physics We prove that the dynamics of the one-dimensional $ XY $ model with random magnetic field perturbed by a sparse set of $ ZZ $ terms with a large coupling constant $ Δ$ gives rise to Lieb-Robinson (L-R) bounds with a logarithmic lightcone and amplitude proportional to $ Δ^{-1} $. These spin systems are equivalent to a set of spinless lattice fermions subjected to a random on site potential and sparse density-density interactions. In the absence of the random magnetic field we also obtain a suppression of the L-R bounds as $ Δ^{-1} $. These results follow from the application of a general theorem about the L-R bound of a generic local time-dependent one-dimensional spin system with local time-dependent perturbations. Adopting the interaction picture of the dynamics, the large and sparse $ ZZ $ perturbations of the $ XY $ model, with or without disorder, are mapped into high-frequency periodic perturbations. All our results are non-perturbative. |
| title | Logarithmic lightcones in the multiparticle Anderson model with sparse interactions |
| topic | Mathematical Physics Disordered Systems and Neural Networks Quantum Physics |
| url | https://arxiv.org/abs/2509.02383 |