Logarithmic lightcones in the multiparticle Anderson model with sparse interactions

Fuente: arXiv
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Autores principales: Toniolo, Daniele, Bose, Sougato
Formato: Preprint
Publicado: 2025
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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