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

doi:10.1016/j.physa.2023.129245

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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(logW)^2−ϵ}, with ϵ<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.

Original language	English
Article number	129245
Journal	Physica A: Statistical Mechanics and its Applications
Volume	631
DOIs	https://doi.org/10.1016/j.physa.2023.129245
Publication status	Published - 5 Oct 2023

Keywords

Ergodicity-breaking
Quantum many-body systems
Thermalization

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10.1016/j.physa.2023.129245

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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(logW)2−ϵ}, with ϵ<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.",

keywords = "Ergodicity-breaking, Quantum many-body systems, Thermalization",

author = "{De Roeck}, Wojciech and Fran{\c c}ois Huveneers and Branko Meeus and Pro{\'s}niak, {Oskar A.}",

note = "Funding Information: W.D.R. and O.P. were supported in part by the FWO (Flemish Research Fund), Belgium under grant G098919N . Publisher Copyright: {\textcopyright} 2023",

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AU - De Roeck, Wojciech

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AU - Meeus, Branko

AU - Prośniak, Oskar A.

PY - 2023/10/5

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N2 - 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(logW)2−ϵ}, with ϵ<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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Rigorous and simple results on very slow thermalization, or quasi-localization, of the disordered quantum chain

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Keywords

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