Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics
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| Format: | Preprint |
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2025
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| _version_ | 1866915680748568576 |
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| author | Giachetti, Guido Defenu, Nicolo |
| author_facet | Giachetti, Guido Defenu, Nicolo |
| contents | We study the the large-$n$ dynamics of the long-range quantum $O(n)$ model, focusing on the strong long-range regime $α<d$. The dynamics of the model exhibits non-trivial features on mesoscopic timescales $t\sim\ln N$, due to the activation of parametric resonances of the nearly degenerate quantum modes. By using recent results establishing the integrability of the large-$n$ limit, we derive the resonance conditions, and construct the reduced multi-mode Hamiltonian that captures the finite-size dynamics. This framework yields the resonance phase diagram and clarifies when and how deviations from mean-field behavior arise. In particular, the presence of multiple resonant modes enhances the logarithmic growth of entanglement and leads to spatially modulated correlations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_14868 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics Giachetti, Guido Defenu, Nicolo Statistical Mechanics Quantum Physics We study the the large-$n$ dynamics of the long-range quantum $O(n)$ model, focusing on the strong long-range regime $α<d$. The dynamics of the model exhibits non-trivial features on mesoscopic timescales $t\sim\ln N$, due to the activation of parametric resonances of the nearly degenerate quantum modes. By using recent results establishing the integrability of the large-$n$ limit, we derive the resonance conditions, and construct the reduced multi-mode Hamiltonian that captures the finite-size dynamics. This framework yields the resonance phase diagram and clarifies when and how deviations from mean-field behavior arise. In particular, the presence of multiple resonant modes enhances the logarithmic growth of entanglement and leads to spatially modulated correlations. |
| title | Large-$n$ $O(n)$ with long-range interactions: integrability and resonance dynamics |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2512.14868 |