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arXiv · 2504.06951

GLT hidden structures in mean-field quantum spin systems

Christiaan J. F. van de Ven·Muhammad Faisal Khan·S. Serra-Capizzano
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Abstract

This work explores structured matrix sequences arising in mean-field quantum spin systems. We express these sequences within the framework of generalized locally Toeplitz (GLT) $*$-algebras, leveraging the fact that each GLT matrix sequence has a unique GLT symbol. This symbol characterizes both the asymptotic singular value distribution and, for Hermitian or quasi-Hermitian sequences, the asymptotic spectral distribution. Specifically, we analyze two cases of real symmetric matrix sequences stemming from mean-field quantum spin systems and determine their associated distributions using GLT theory. Our study concludes with visualizations and numerical tests that validate the theoretical findings, followed by a discussion of open problems and future directions.

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Christiaan J. F. van de Ven, Muhammad Faisal Khan, S. Serra-Capizzano. 2025-04-09. GLT hidden structures in mean-field quantum spin systems. https://arxiv.org/abs/2504.06951

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