Abstract
We study Hilbert-space localization of the many-body dynamics due to ergodicity breaking and analyze this effect in terms of the entanglement entropy and the entanglement spectrum. We find a transition from a regime driven by quantum tunneling to a regime that is dominated by boson-boson interaction, where the latter exhibits ergodicity breaking. Properties of this transition are captured by observation time averaging, which effectively suppresses the large dynamical entanglement fluctuations near the critical point. We employ this approach to the experimentally available bosonic Josephson junction. In this example, the transition from a tunneling regime to Hilbert-space localization reveals clear signatures in the entanglement entropy and entanglement spectrum. Interestingly, the transition point is reduced by quantum effects in comparison to the well-known result of the mean-field approximation in the form of self-trapping. This indicates that quantum fluctuations reduce the classical self-trapping. Different scaling with respect to the number of bosons, N, is found in the tunneling and the localization regime: While the entanglement entropy grows logarithmically with N in the tunneling regime, it increases linearly in the localized regime. Our results indicate that entanglement provides a concept for a sensitive diagnosis for the transition from a quantum tunneling regime to Hilbert-space localization.
Original language | English |
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Article number | 012413 |
Journal | Physical Review A |
Volume | 107 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2023 |
Bibliographical note
Publisher Copyright:© 2023 American Physical Society.
Funding
We are grateful to Eli Barkai for the useful discussions. Q.L. thanks Qiming Ding and Qiang Miao for illuminating discussions. This research is supported by the Israel Science Foundation through Grant No. 1614/21 (Q.L.) and by a grant of the Julian Schwinger Foundation for Physics Research (K.Z.).
Funders | Funder number |
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Julian Schwinger Foundation for Physics Research | |
Israel Science Foundation | 1614/21 |