Logarithmic lightcones in the multiparticle Anderson model with sparse interactions

• URL: http://arxiv.org/abs/2509.02383v1
• Date: Tue, 02 Sep 2025 14:50:17 GMT
• Title: Logarithmic lightcones in the multiparticle Anderson model with sparse interactions
• Authors: Daniele Toniolo, Sougato Bose,
• Abstract summary: We prove that the dynamics of the one-dimensional $ XY $ model with random magnetic field perturbed by a sparse set of $ ZZ $ terms gives rise to Lieb-Robinson bounds.<n>In the absence of the random magnetic field we also obtain a suppression of the L-R bounds as $ Delta-1 $.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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