Logarithmic lightcones in the multiparticle Anderson model with sparse interactions

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} $. To obtain these results we prove a theorem about the effect of compactly supported time-dependent perturbations on the L-R bound of a generic local time-dependent one-dimensional spin systems. 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.

Mathematical Physics (math-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Physics (quant-ph)

arXiv:2509.02383 [math-ph]

(or arXiv:2509.02383v2 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2509.02383 Focus to learn more arXiv-issued DOI via DataCite

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