How a Small Quantum Bath Can Thermalize Long Localized Chains

Physical Review Letters
David J LuitzWojciech De Roeck

Abstract

We investigate the stability of the many-body localized phase for a system in contact with a single ergodic grain modeling a Griffiths region with low disorder. Our numerical analysis provides evidence that even a small ergodic grain consisting of only three qubits can delocalize a localized chain as soon as the localization length exceeds a critical value separating localized and extended regimes of the whole system. We present a simple theory, consistent with De Roeck and Huveneers's arguments in [Phys. Rev. B 95, 155129 (2017)PRBMDO2469-995010.1103/PhysRevB.95.155129] that assumes a system to be locally ergodic unless the local relaxation time determined by Fermi's golden rule is larger than the inverse level spacing. This theory predicts a critical value for the localization length that is perfectly consistent with our numerical calculations. We analyze in detail the behavior of local operators inside and outside the ergodic grain and find excellent agreement of numerics and theory.

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Citations

Jun 5, 2018·Reports on Progress in Physics·S A Parameswaran, Romain Vasseur
Nov 1, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Pedro PonteA Chandran
Nov 1, 2017·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·Wojciech De Roeck, John Z Imbrie
Jan 13, 2019·Physical Review Letters·Zala LenarčičAchim Rosch
Jun 6, 2020·Physical Review Letters·Giuseppe De Tomasi, Ivan M Khaymovich
Jun 25, 2020·Physical Review. E·Petr BraunThomas Guhr
Apr 19, 2018·Proceedings of the National Academy of Sciences of the United States of America·Marko Žnidarič, Marko Ljubotina
Oct 20, 2018·Physical Review Letters·Thimothée ThieryWojciech De Roeck
Aug 31, 2018·Proceedings of the National Academy of Sciences of the United States of America·William BerdanierRomain Vasseur
Aug 7, 2019·Physical Review Letters·Ling-Na Wu, André Eckardt
Sep 26, 2020·Physical Review Letters·Zala LenarčičEhud Altman
Feb 6, 2021·Physical Review Letters·Ulrich KrauseMichele Filippone
Mar 31, 2021·Physical Review Letters·Rahul SahayNorman Y Yao

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