GLT hidden structures in mean-field quantum spin systems

Morgenshtern V, Khan MF, Serra-Capizzano S (2026)

Publication Status: Submitted

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2026

DOI: 10.48550/arXiv.2504.06951

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 the-

ory. Our study concludes with visualizations and numerical tests that validate the theoretical findings,

followed by a discussion of open problems and future directions.

Authors with CRIS profile

Veniamin Morgenshtern Professur für Maschinelles Lernen in der Signalverarbeitung

Involved external institutions

Uppsala University SE Sweden (SE) University of Insubria / Università degli Studi dell'Insubria IT Italy (IT)

How to cite

APA:

Morgenshtern, V., Khan, M.F., & Serra-Capizzano, S. (2026). GLT hidden structures in mean-field quantum spin systems. (Unpublished, Submitted).

MLA:

Morgenshtern, Veniamin, Muhammad Faisal Khan, and S. Serra-Capizzano. GLT hidden structures in mean-field quantum spin systems. Unpublished, Submitted. 2026.

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