Integrability sensitivity of genuine multi-entropy at large system size

Determine whether the apparent insensitivity of the genuine second-Rényi multi-entropy to integrability breaking in interacting periodic fermion chains is genuine or instead a finite-size effect that would disappear at large system size.

Background

The paper compares the time evolution of genuine second-Rényi multi-entropy and mutual information in free, Bethe-integrable, and non-integrable periodic fermion chains. For the small system size accessible to exact diagonalization, the integrable and non-integrable cases have nearly indistinguishable plateau values and fluctuation amplitudes. The authors therefore cannot determine whether genuine multi-entropy is insensitive to integrability breaking or whether the observed agreement results from finite-size limitations.

References

However, given the small system size ($N=8$) accessible to exact diagonalization, it remains unclear whether this reflects a genuine insensitivity of $\textrm{GM}_2{(3)}$ to integrability breaking or merely a finite-size effect that would be resolved at large $N$.

— Growing Einstein-Rosen Bridge with Multi-partite Entanglement  (2609.18225 - Anegawa et al., 16 Sep 2026) in Section 4, “Spin systems”