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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.01727 |
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| _version_ | 1866913339934769152 |
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| author | Brodskiy, Michael Howell, Owen L. |
| author_facet | Brodskiy, Michael Howell, Owen L. |
| contents | Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of identical vector spaces we motivate natural generalizations of the Gaussian Ensemble family. We show how the k-fold invariant constraints are satisfied in both disordered spin models and systems with gauge symmetries, specifically quantum double models. We use Schur-Weyl duality to completely characterize the form of allowed Gaussian distributions satisfying k-fold invariant constraints. The eigenvalue distribution of our proposed ensembles is computed exactly using the Harish-Chandra integral method. For the 2-fold tensor product case, we show that the derived distribution couples eigenvalue spectrum to entanglement spectrum. Guided by representation theory, our work is a natural extension of the standard Gaussian random matrix ensembles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01727 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | k-Fold Gaussian Random Matrix Ensembles I: Forcing Structure into Random Matrices Brodskiy, Michael Howell, Owen L. Mathematical Physics Representation Theory Random Matrix Theory is a powerful tool in applied mathematics. Three canonical models of random matrix distributions are the Gaussian Orthogonal, Unitary and Symplectic Ensembles. For matrix ensembles defined on k-fold tensor products of identical vector spaces we motivate natural generalizations of the Gaussian Ensemble family. We show how the k-fold invariant constraints are satisfied in both disordered spin models and systems with gauge symmetries, specifically quantum double models. We use Schur-Weyl duality to completely characterize the form of allowed Gaussian distributions satisfying k-fold invariant constraints. The eigenvalue distribution of our proposed ensembles is computed exactly using the Harish-Chandra integral method. For the 2-fold tensor product case, we show that the derived distribution couples eigenvalue spectrum to entanglement spectrum. Guided by representation theory, our work is a natural extension of the standard Gaussian random matrix ensembles. |
| title | k-Fold Gaussian Random Matrix Ensembles I: Forcing Structure into Random Matrices |
| topic | Mathematical Physics Representation Theory |
| url | https://arxiv.org/abs/2405.01727 |