GLT hidden structures in mean-field quantum spin systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916687334342656 |
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| author | van de Ven, Christiaan J. F. Khan, Muhammad Faisal Serra-Capizzano, S. |
| author_facet | van de Ven, Christiaan J. F. Khan, Muhammad Faisal Serra-Capizzano, S. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_06951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GLT hidden structures in mean-field quantum spin systems van de Ven, Christiaan J. F. Khan, Muhammad Faisal Serra-Capizzano, S. Quantum Physics Numerical Analysis 46L65, 15B05, 15A18 (81R30, 82B20) 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. |
| title | GLT hidden structures in mean-field quantum spin systems |
| topic | Quantum Physics Numerical Analysis 46L65, 15B05, 15A18 (81R30, 82B20) |
| url | https://arxiv.org/abs/2504.06951 |