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

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.

71 pages, 5 figures; v1-->v2: The introduction is rewritten to include the following additions: additional references, extensive literature review (comparing the result with other relevant math phys works), detailed explanation of the proof, remarks about the result and proof method. In the bulk many inconsequential errors have been corrected, and the text is edited to increase readability