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

The present work examines how effective-model-space calculations of nuclear many-body systems are able to rearrange and converge multi-particle entanglement, and information more generally. The generalized Lipkin-Meshkov-Glick (LMG) model is considered here as a demonstration, 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 to an effective model space, together with a variational rotation of the qubits (spins), which constitute the relevant elementary degrees of freedom in this model. The non-commutivity of the rotation and truncation allow for an exponential improvement of the energy convergence throughout much of the model space, compared with truncations without rotations, as we have shown previously in the reduced LMG model. Our analysis is extended to examine measures of correlations and entanglement, and to quantify their convergence with increasing cut-off. We focus on one- and two-spin entanglement entropies, mutual information, as well as n-tangles for n=2, 4 to estimate multi-body entanglement. The effective description is found to provide “minimal” entropies and mutual information of the rotated spins, while, at the same time, 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 found to be more difficult to capture with the EMS description, the improvement in convergence, compared to truncations of the bare Hamiltonian, is significantly more dramatic. Finally, we investigate how spin squeezing, which is particularly sensitive to entanglement details of the system, is reproduced by quantum simulations of the LMG model we previously performed using IBM’s quantum computers. We conclude that the low-energy effective model space 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 that are closer to nature. We anticipate our results have import for effective field theories relevant to high-energy physics and nuclear physics more broadly.

This work was supported, in part, by Universit ̈at Bielefeld and ERC- 885281-KILONOVA Advanced Grant, and, in part, by U.S. Department of Energy, Office of Science, Office of Nuclear Physics, InQubator for Quantum Simulation (IQuS) under Award Number DOE (NP) Award DE-SC0020970 via the program on Quantum Horizons: QIS Research and Innovation for Nuclear Science.