The Simplicial Bridge: Mapping quantum multi-spin exchange to higher-order topological networks in continuous magnetic fields
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910129910185984 |
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| author | Yadav, Alok |
| author_facet | Yadav, Alok |
| contents | The macroscopic dynamics of topological defects in magnetic materials are traditionally modeled using pairwise interactions. However, higher-order quantum exchange mechanisms - such as biquadratic and 4-spin ring exchange-play a critical role in strongly correlated systems. In this work, we introduce the "Simplicial Bridge," an exact analytical framework that maps these high-dimensional, non-linear Landau-Lifshitz partial differential equations onto generalized Kuramoto phase-oscillator networks operating on abstract simplicial complexes. We rigorously demonstrate that spatial overlap in the continuous limit natively generates higher-order topological forces without requiring a supportive discrete atomic lattice. Specifically, the overlap of 1D helimagnetic kinks generates 2-simplices (triadic forces), while the spatial compression of 2D skyrmion tails - governed by modified Bessel function asymptotics - generates true 3-simplices (tetradic forces). Furthermore, we establish that the higher-order spatial derivatives inherent to these multi-spin interactions provide an intrinsic energetic barrier that bypasses Derrick's Theorem, stabilizing 2D topological solitons without the strict need for Dzyaloshinskii-Moriya Interaction (DMI). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10773 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Simplicial Bridge: Mapping quantum multi-spin exchange to higher-order topological networks in continuous magnetic fields Yadav, Alok Pattern Formation and Solitons Mesoscale and Nanoscale Physics Statistical Mechanics Adaptation and Self-Organizing Systems The macroscopic dynamics of topological defects in magnetic materials are traditionally modeled using pairwise interactions. However, higher-order quantum exchange mechanisms - such as biquadratic and 4-spin ring exchange-play a critical role in strongly correlated systems. In this work, we introduce the "Simplicial Bridge," an exact analytical framework that maps these high-dimensional, non-linear Landau-Lifshitz partial differential equations onto generalized Kuramoto phase-oscillator networks operating on abstract simplicial complexes. We rigorously demonstrate that spatial overlap in the continuous limit natively generates higher-order topological forces without requiring a supportive discrete atomic lattice. Specifically, the overlap of 1D helimagnetic kinks generates 2-simplices (triadic forces), while the spatial compression of 2D skyrmion tails - governed by modified Bessel function asymptotics - generates true 3-simplices (tetradic forces). Furthermore, we establish that the higher-order spatial derivatives inherent to these multi-spin interactions provide an intrinsic energetic barrier that bypasses Derrick's Theorem, stabilizing 2D topological solitons without the strict need for Dzyaloshinskii-Moriya Interaction (DMI). |
| title | The Simplicial Bridge: Mapping quantum multi-spin exchange to higher-order topological networks in continuous magnetic fields |
| topic | Pattern Formation and Solitons Mesoscale and Nanoscale Physics Statistical Mechanics Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2604.10773 |