  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 $n=2,4$ 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.
