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arXiv · 2509.02383

Logarithmic lightcones in the multiparticle Anderson model with sparse interactions

Daniele Toniolo·Sougato Bose
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Abstract

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 $ \Delta $ gives rise to Lieb-Robinson (L-R) bounds with a logarithmic lightcone and amplitude proportional to $ \Delta^{-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 $ \Delta^{-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.

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Daniele Toniolo, Sougato Bose. 2025-09-02. Logarithmic lightcones in the multiparticle Anderson model with sparse interactions. https://arxiv.org/abs/2509.02383

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