https://doi.org/10.1140/epja/s10050-023-01145-x
Regular Article - Theoretical Physics
Multi-body entanglement and information rearrangement in nuclear many-body systems: a study of the Lipkin–Meshkov–Glick model
1
Fakultät für Physik, Universität Bielefeld, 33615, Bielefeld, Germany
2
GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291, Darmstadt, Germany
3
InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, 98195, Seattle, WA, USA
b
crobin@physik.uni-bielefeld.de
Received:
28
June
2023
Accepted:
29
September
2023
Published online:
17
October
2023
We examine how effective-model-space (EMS) calculations of nuclear many-body systems rearrange and converge multi-particle entanglement. The generalized Lipkin–Meshkov–Glick (LMG) model is used to motivate and provide insight for future developments of entanglement-driven descriptions of nuclei. The effective approach is based on a truncation of the Hilbert space together with a variational rotation of the qubits (spins), which constitute the relevant elementary degrees of freedom. The non-commutivity of the rotation and truncation allows for an exponential improvement of the energy convergence throughout much of the model space. Our analysis examines measures of correlations and entanglement, and quantifies their convergence with increasing cut-off. We focus on one- and two-spin entanglement entropies, mutual information, and n-tangles for 
to estimate multi-body entanglement. The effective description strongly suppresses entropies and mutual information of the rotated spins, while being able to recover the exact results to a large extent with low cut-offs. Naive truncations of the bare Hamiltonian, on the other hand, artificially underestimate these measures. The n-tangles in the present model provide a basis-independent measures of n-particle entanglement. While these are more difficult to capture with the EMS description, the improvement in convergence, compared to truncations of the bare Hamiltonian, is significantly more dramatic. We conclude that the low-energy EMS techniques, that successfully provide predictive capabilities for low-lying observables in many-body systems, exhibit analogous efficacy for quantum correlations and multi-body entanglement in the LMG model, motivating future studies in nuclear many-body systems and effective field theories relevant to high-energy physics and nuclear physics.
Martin J. Savage: On leave from the Institute for Nuclear Theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
