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We examine how effective-model-space (EMS) calculations of nuclear many-bodysystems rearrange and converge multi-particle entanglement. The generalizedLipkin-Meshkov-Glick (LMG) model is used to motivate and provide insight forfuture developments of entanglement-driven descriptions of nuclei. Theeffective approach is based on a truncation of the Hilbert space together witha variational rotation of the qubits (spins), which constitute the relevantelementary degrees of freedom. The non-commutivity of the rotation andtruncation allows for an exponential improvement of the energy convergencethroughout much of the model space. Our analysis examines measures ofcorrelations and entanglement, and quantifies their convergence with increasingcut-off. We focus on one- and two-spin entanglement entropies, mutualinformation, and $n$-tangles for $n=2,4$ to estimate multi-body entanglement.The effective description strongly suppresses entropies and mutual informationof the rotated spins, while being able to recover the exact results to a largeextent with low cut-offs. Naive truncations of the bare Hamiltonian, on theother hand, artificially underestimate these measures. The $n$-tangles in thepresent model provide a basis-independent measures of $n$-particleentanglement. While these are more difficult to capture with the EMSdescription, the improvement in convergence, compared to truncations of thebare Hamiltonian, is significantly more dramatic. We conclude that thelow-energy EMS techniques, that successfully provide predictive capabilitiesfor low-lying observables in many-body systems, exhibit analogous efficacy forquantum correlations and multi-body entanglement in the LMG model, motivatingfuture studies in nuclear many-body systems and effective field theoriesrelevant to high-energy physics and nuclear physics.

Multi-Body Entanglement and Information Rearrangement in Nuclear Many-Body Systems