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arXiv · 2308.08462

Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain

Wojciech De Roeck·François Huveneers·Branko Meeus·Oskar A. Prośniak
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Abstract

This paper originates from lectures delivered at the summer school "Fundamental Problems in Statistical Physics XV" in Bruneck, Italy, in 2021. We give a brief and limited introduction into ergodicity-breaking induced by disorder. As the title suggests, we include a simple yet rigorous and original result: For a strongly disordered quantum chain, we exhibit a full set of quasi-local quantities whose dynamics is negligible up to times of order $\exp\{ c (\log W)^{2-\epsilon}\}$, with $\epsilon < 1$, $c$ a numerical constant, and $W$ the disorder strength. Such a result, that is often referred to as "quasi-localization", can in principle be obtained in other systems as well, but for a disordered quantum chain, its proof is relatively short and transparent.

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Wojciech De Roeck, François Huveneers, Branko Meeus, Oskar A. Prośniak. 2023-08-16. Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain. https://arxiv.org/abs/2308.08462

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