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

TL;DR

This paper proves that the Quantum Sun model exhibits localization with Poisson spectral statistics when the coupling parameter is sufficiently small, demonstrating genuine many-body localization with limited disorder variables.

Contribution

It provides a rigorous proof of localization and Poisson statistics in a genuine many-body quantum model with logarithmically growing disorder variables.

Findings

Model is localized for small alpha

Spectral statistics are Poissonian in this regime

Disorder variables grow logarithmically with system size

Abstract

The Quantum Sun model is a many-body Hamiltonian model of interacting spins arranged on the half-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 is Poissonian. The main interest of this result is that the model is a genuine many-body model. In particular, the number of independent disorder variables grows only logarithmically with the Hilbert space dimension.