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arXiv · 1709.10313

Non-Ergodic Delocalization in the Rosenzweig-Porter Model

Per von Soosten·Simone Warzel
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Abstract

We consider the Rosenzweig-Porter model $H = V + \sqrt{T}\, Φ$, where $V$ is a $N \times N$ diagonal matrix, $Φ$ is drawn from the $N \times N$ Gaussian Orthogonal Ensemble, and $N^{-1} \ll T \ll 1$. We prove that the eigenfunctions of $H$ are typically supported in a set of approximately $NT$ sites, thereby confirming the existence of a previously conjectured non-ergodic delocalized phase. Our proof is based on martingale estimates along the characteristic curves of the stochastic advection equation satisfied by the local resolvent of the Brownian motion representation of $H$.

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Per von Soosten, Simone Warzel. 2018-06-27. Non-Ergodic Delocalization in the Rosenzweig-Porter Model. https://doi.org/10.1007/s11005-018-1131-7

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