Eigenstate entanglement in integrable collective spin models

TL;DR

This paper investigates how the average entanglement entropy of energy eigenstates in collective spin models, especially the Lipkin-Meshov-Glick model, can serve as a diagnostic for quantum integrability, showing that non-maximal values indicate integrability.

Contribution

The study analytically and numerically demonstrates that the average entanglement entropy converges to half of its maximum in the thermodynamic limit for integrable collective spin models, providing a potential diagnostic tool.

Findings

Average EE converges to 1/2 of maximum in the thermodynamic limit.

Universal behavior of average EE across parameters in the LMG model.

Non-maximal EE values can indicate quantum integrability.

Abstract

The average entanglement entropy (EE) of the energy eigenstates in non-vanishing partitions has been recently proposed as a diagnostic of integrability in quantum many-body systems. For it to be a faithful characterization of quantum integrability, it should distinguish quantum systems with a well-defined classical limit in the same way as the unequivocal classical integrability criteria. We examine the proposed diagnostic in the class of collective spin models characterized by permutation symmetry in the spins. The well-known Lipkin-Meshov-Glick (LMG) model is a paradigmatic integrable system in this class with a well-defined classical limit. Thus, this model is an excellent testbed for examining quantum integrability diagnostics. First, we calculate analytically the average EE of the Dicke basis $\{|j,m\rangle \}_{m=-j}^j$ in any non-vanishing bipartition, and show that in the thermodynamic limit, it converges to $1/2$ of the maximal EE in the corresponding bipartition. Using finite-size scaling, we numerically demonstrate that the aforementioned average EE in the thermodynamic limit is universal for all parameter values of the LMG model. Our analysis illustrates how a value of the average EE far away from the maximal in the thermodynamic limit could be a signature of integrability.