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arXiv · 2506.13511

Many-body Localization and Poisson statistics in the Quantum Sun model

Wojciech De Roeck·Amirali Hannani
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Abstract

The Quantum Sun model is a many-body Hamiltonian model of interacting spins arranged on the half-line (or the line). Spins at distance $n$ from the origin are coupled to the rest of the system via a term of strength $\alpha^n$, with $\alpha \in (0,1)$. From theoretical and numerical considerations, it is believed that this model undergoes a localization-delocalization transition at the critical value $\alpha=\frac{1}{\sqrt{2}}$. We prove that, for $\alpha \ll \frac{1}{\sqrt{2}}$, the model is localized and that its spectral statistics are Poissonian. The main novelty of this result is that the model considered here is a genuine many-body model, in which the interaction has a profound effect.

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Wojciech De Roeck, Amirali Hannani. 2025-06-16. Many-body Localization and Poisson statistics in the Quantum Sun model. https://arxiv.org/abs/2506.13511

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