Semiclassical picture of the Heisenberg spin glass in two dimensions: from weak localization to hydrodynamics
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915883635441664 |
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| author | Bracci-Testasecca, Giacomo Niedda, Jacopo Coraggio, Aldo Moessner, Roderich Scardicchio, Antonello |
| author_facet | Bracci-Testasecca, Giacomo Niedda, Jacopo Coraggio, Aldo Moessner, Roderich Scardicchio, Antonello |
| contents | The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of its spectrum and eigenfunctions. We find that the nature of the spin-wave excitations, whether they are hydrodynamic or localized modes, depends crucially on the relevance/irrelevance - in the renormalization group sense - of the correlations induced by the underlying classical order in the spin-wave Hamiltonian matrix elements: low-energy excitations around magnetically ordered states are delocalized, whereas those around spin-glass ordered states are localized, albeit weakly. Remarkably, in the magnetically ordered case, spin-wave delocalization is robust with respect to the presence of disorder, even in two spatial dimensions. We interpret this phenomenology by relating the spontaneous breaking of spin-rotation symmetry in the original Heisenberg model to the symmetry and universality class of the resulting quadratic spin-wave Hamiltonian. We conjecture that the hydrodynamic picture can be recovered through the inclusion of interactions among the spin-wave excitations at higher order in the semiclassical expansion, favoring the onset of ergodic behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiclassical picture of the Heisenberg spin glass in two dimensions: from weak localization to hydrodynamics Bracci-Testasecca, Giacomo Niedda, Jacopo Coraggio, Aldo Moessner, Roderich Scardicchio, Antonello Disordered Systems and Neural Networks The two-dimensional Heisenberg spin-glass model is investigated by means of a semiclassical expansion around classical states. At leading order, we obtain an effective quadratic spin-wave Hamiltonian and study the localization properties of its spectrum and eigenfunctions. We find that the nature of the spin-wave excitations, whether they are hydrodynamic or localized modes, depends crucially on the relevance/irrelevance - in the renormalization group sense - of the correlations induced by the underlying classical order in the spin-wave Hamiltonian matrix elements: low-energy excitations around magnetically ordered states are delocalized, whereas those around spin-glass ordered states are localized, albeit weakly. Remarkably, in the magnetically ordered case, spin-wave delocalization is robust with respect to the presence of disorder, even in two spatial dimensions. We interpret this phenomenology by relating the spontaneous breaking of spin-rotation symmetry in the original Heisenberg model to the symmetry and universality class of the resulting quadratic spin-wave Hamiltonian. We conjecture that the hydrodynamic picture can be recovered through the inclusion of interactions among the spin-wave excitations at higher order in the semiclassical expansion, favoring the onset of ergodic behavior. |
| title | Semiclassical picture of the Heisenberg spin glass in two dimensions: from weak localization to hydrodynamics |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2603.22077 |