GLT hidden structures in mean-field quantum spin systems

This work investigates structured matrix sequences arising from mean-field quantum spin systems. We embed these sequences into the framework of generalized locally Toeplitz (GLT) ∗-algebras, exploiting the fact that every GLT matrix sequence is associated with a unique GLT symbol. This symbol determines the asymptotic singular value distribution and, in the Hermitian or quasi-Hermitian setting, the asymptotic spectral distribution of the sequence. We focus on two classes of real symmetric matrix sequences derived from mean-field quantum spin models and characterize their limiting spectral distributions through GLT theory. The theoretical results are complemented by numerical experiments and visualizations that confirm the predicted asymptotic behaviour. We conclude with a discussion of open problems and directions for future research.