Reviving product states in the disordered Heisenberg chain

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Original languageEnglish
Article number5847
JournalNature Communications
Volume14
Publication statusPublished - 20 Sept 2023

Abstract

When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.

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Reviving product states in the disordered Heisenberg chain. / Wilming, Henrik; Osborne, Tobias J.; Decker, Kevin S.C. et al.
In: Nature Communications, Vol. 14, 5847, 20.09.2023.

Research output: Contribution to journalArticleResearchpeer review

Wilming H, Osborne TJ, Decker KSC, Karrasch C. Reviving product states in the disordered Heisenberg chain. Nature Communications. 2023 Sept 20;14:5847. doi: 10.48550/arXiv.2210.03153, 10.1038/s41467-023-41464-7
Wilming, Henrik ; Osborne, Tobias J. ; Decker, Kevin S.C. et al. / Reviving product states in the disordered Heisenberg chain. In: Nature Communications. 2023 ; Vol. 14.
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abstract = "When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.",
author = "Henrik Wilming and Osborne, {Tobias J.} and Decker, {Kevin S.C.} and Christoph Karrasch",
note = "Funding Information: H.W. would like to thank Merlin F{\"u}llgraf and Daniel Burgarth for useful discussions and Berislav Bu{\v c}a for comments on an earlier version of the manuscript. We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1227 (DQ-mat) (T.J.O.), Quantum Valley Lower Saxony (T.J.O.), and under Germany{\textquoteright}s Excellence Strategy EXC-2123 QuantumFrontiers 390837967 (H.W., T.J.O., C.K.). Moreover, we acknowledge support by {\textquoteleft}Nieders{\"a}chsisches Vorab{\textquoteright} through the {\textquoteleft}Quantum- and Nano-Metrology (QUANOMET){\textquoteright} initiative within the project P-1 (C.K., K.S.C.D.). ",
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AU - Wilming, Henrik

AU - Osborne, Tobias J.

AU - Decker, Kevin S.C.

AU - Karrasch, Christoph

N1 - Funding Information: H.W. would like to thank Merlin Füllgraf and Daniel Burgarth for useful discussions and Berislav Buča for comments on an earlier version of the manuscript. We acknowledge support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1227 (DQ-mat) (T.J.O.), Quantum Valley Lower Saxony (T.J.O.), and under Germany’s Excellence Strategy EXC-2123 QuantumFrontiers 390837967 (H.W., T.J.O., C.K.). Moreover, we acknowledge support by ‘Niedersächsisches Vorab’ through the ‘Quantum- and Nano-Metrology (QUANOMET)’ initiative within the project P-1 (C.K., K.S.C.D.).

PY - 2023/9/20

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N2 - When a generic quantum system is prepared in a simple initial condition, it typically equilibrates toward a state that can be described by a thermal ensemble. A known exception is localized systems that are non-ergodic and do not thermalize; however, local observables are still believed to become stationary. Here we demonstrate that this general picture is incomplete by constructing product states that feature periodic high-fidelity revivals of the full wavefunction and local observables that oscillate indefinitely. The system neither equilibrates nor thermalizes. This is analogous to the phenomenon of weak ergodicity breaking due to many-body scars and challenges aspects of the current phenomenology of many-body localization, such as the logarithmic growth of the entanglement entropy. To support our claim, we combine analytic arguments with large-scale tensor network numerics for the disordered Heisenberg chain. Our results hold for arbitrarily long times in chains of 160 sites up to machine precision.

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